OpenLLM-France/wikimedia huggingface dataset:
# Scouting/BSA/Sculpture Merit Badge
## Requirement 1

Explain to your counselor the precautions that must be followed for the safe use and operation of a sculptor's tools, equipment, and other materials.

## Requirement 2

Do TWO of the following:
    A. Model in clay a life-sized human head. Then sculpt in modeling clay (such as Plastine or Sculpey) or carve/rasp in wood or soft stone a small-scale model of an animal or person. Explain to your counselor the method and tools you used to sculpt the figure.
    B. Make a plaster mold of a fruit or vegetable. In this mold make a copy of the fruit or vegetable. Explain to your counselor the method and tools you used to make the copy.
    C. With your parent's permission and your counselor's approval, visit a museum, art exhibit, art gallery, artists' co-op, or artist's studio. After your visit, share with your counselor what you have learned. Discuss the importance of visual arts and how it strengthens social tolerance and helps stimulate cultural, intellectual, and personal development.

## Requirement 3

Find out about career opportunities in sculpture. Pick one and find out the education, training, and experience required for this profession. Discuss this with your counselor, and explain why this profession might interest you.

## External links

* Sculpture Merit Badge with Workbook PDF, current requirements, and resources.
* Earning Merit Badges in the Boy Scouts of America
* Indoor Hobbies and Arts and Crafts
* Art | Basketry | Bugling | Coin Collecting | Collections | Cooking | Dog Care | Fingerprinting | Genealogy | Indian Lore | Leatherwork | Model Design and Building | Moviemaking | Music | Painting | Pets | Photography | Pottery | Programming | Radio | Railroading | Reading | Sculpture | Stamp Collecting | Theater | Wood Carving | Woodwork
# Pokémon/Pokédex/Tauros
## Basic Statistics

* National Index: 128
* Johto Index: 148
* Hoenn Index: 285
* Stage: Basic
* Height: 1.4 meters (4.6 ft)
* Weight: 88.4 kilograms (195 lb)
* Gender Distribution: 100% Male
* Ability: Intimidate
* Type: Normal
* Species: Wild Bull
* Egg Group: Ground
* Hatch Steps: 5120
* Catch Rate: 45
* Base Experience: 211
* Max Experience: 1250000
| | HP | Attack | Defense | Speed | Special Attack | Special Defense |
| Base Stats (RB/Y) | 75 | 100 | 95 | 110 | 70 | 70 |
| Base Stats (GS/C) | 75 | 100 | 95 | 110 | 40 | 70 |
| Base Stats (RS/FL/E) | 75 | 100 | 95 | 110 | 40 | 70 |
| Base Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Base Stats (BW/B2W2) | – | – | – | – | – | – |
| Base Stats (XY/ORAS) | – | – | – | – | – | – |
| Base Stats (SM/USUM) | – | – | – | – | – | – |
| Base Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Max Stats (RB/Y) | 353 | 298 | 288 | 318 | 238 | 238 |
| Max Stats (GS/C) | 353 | 298 | 288 | 318 | 178 | 238 |
| Max Stats (RS/FL/E) | 354 | 328 | 317 | 350 | 196 | 262 |
| Max Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Max Stats (B/W/B2W2) | – | – | – | – | – | – |
| Max Stats (X/Y/ORAS) | – | – | – | – | – | – |
| Max Stats (SM/USUM) | – | – | – | – | – | – |
| Max Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Effort Points (Sword/Shield/BDSP) | – | – | – | – | – | – |

## Type Matching

Move types which are good on Tauros: Fighting Move types which don't effect Tauros: Ghost
All other move types are normal effectiveness on Tauros.

## Moveset

| Level | Red / Blue | Yellow | Gold / Silver | Crystal | Ruby / Sapphire Emerald XD / Colosseum | Fire Red / Leaf Green |
| Start | Tackle | Tackle | Tackle | Tackle | Tackle | Tackle Tail Whip |
| 4 | - | - | Tail Whip | Tail Whip | Tail Whip | Rage |
| 8 | - | - | Rage | Rage | Rage | Horn Attack |
| 13 | - | - | Horn Attack | Horn Attack | Horn Attack | Scary Face |
| 19 | - | - | Scary Face | Scary Face | Scary Face | Pursuit |
| 21 | Stomp | Stomp | - | - | - | - |
| 26 | - | - | Pursuit | Pursuit | Pursuit | Swagger |
| 28 | Tail Whip | Tail Whip | - | - | - | - |
| 34 | - | - | Rest | Rest | Rest | Rest |
| 35 | Leer | Leer | - | - | - | - |
| 43 | - | - | Thrash | Thrash | Thrash | Thrash |
| 44 | Rage | Rage | - | - | - | - |
| 51 | Take Down | Take Down | - | - | - | - |
| 53 | - | - | Take Down | Take Down | Take Down | Take Down |

### TM/HM

* RB/Y/GS/C/RS/FL: Blizzard, Double Team, Earthquake, Fire Blast, Hyper Beam, Rest, Strength, Thunder, Toxic
* RB/Y/C/RS/FL: Ice Beam, Thunderbolt
* GS/C/RS/FL: Attract, Frustration, Hidden Power, Iron Tail, Protect, Return, Rock Smash, Sunny Day, Surf
* C/RS/FL: Flamethrower
* RB/Y: Bide, Body Slam, Double-Edge, Fissure, Horn Drill, Mimic, Rage, Skull Bash, Substitute, Take Down
* GS/C: Curse, Endure, Headbutt, Icy Wind, Sleep Talk, Snore, Swagger, Zap Cannon
* RS/FL: Facade, Rain Dance, Rock Tomb, Sandstorm, Secret Power, Shock Wave, Solarbeam, Water Pulse

## Trading Cards

* Jungle #47 - Tauros
* Gym Heroes #64 - Blaine's Tauros
* Expedition #133 - Tauros
* EX FireRed & LeafGreen #16 - Tauros
# Pokémon/Pokédex/Teddiursa
## Basic Statistics

* National Index: 216
* Johto Index: 193
* Hoenn Index: 358
* Stage: Basic
* Height: 0.6m/2'0"
* Weight: 8.8kg/19.0lb
* Gender Distribution: 50% Male
* Ability: Pickup
* Type: Normal
* Species: Little Bear
* Egg Group: Ground
* Hatch Steps: 5120
* Catch Rate: 120
* Base Experience: 124
* Max Experience: 1000000
| | HP | Attack | Defense | Speed | Special Attack | Special Defense |
| Base Stats (RB/Y) | - | - | - | - | - | - |
| Base Stats (GS/C) | 60 | 80 | 50 | 40 | 50 | 50 |
| Base Stats (RS/FL/E) | 60 | 80 | 50 | 40 | 50 | 50 |
| Base Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Base Stats (BW/B2W2) | – | – | – | – | – | – |
| Base Stats (XY/ORAS) | – | – | – | – | – | – |
| Base Stats (SM/USUM) | – | – | – | – | – | – |
| Base Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Max Stats (RB/Y) | - | - | - | - | - | - |
| Max Stats (GS/C) | 323 | 258 | 198 | 178 | 198 | 198 |
| Max Stats (RS/FL/E) | 324 | 284 | 218 | 196 | 218 | 218 |
| Max Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Max Stats (B/W/B2W2) | – | – | – | – | – | – |
| Max Stats (X/Y/ORAS) | – | – | – | – | – | – |
| Max Stats (SM/USUM) | – | – | – | – | – | – |
| Max Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Effort Points (Sword/Shield/BDSP) | – | – | – | – | – | – |

## Type Matching

Move types which are good on Teddiursa: Fighting Move types which don't effect Teddiursa: Ghost
All other move types are normal effectiveness on Teddiursa.

## Moveset

| Level | Gold / Silver | Crystal | Ruby / Sapphire | Fire Red / Leaf Green |
| Start | Scratch Leer | Scratch Leer | Scratch Leer | Scratch Leer |
| 7 | - | - | Lick | Lick |
| 8 | Lick | Lick | - | - |
| 13 | - | - | Fury Swipes | Fury Swipes |
| 15 | Fury Swipes | Fury Swipes | - | - |
| 19 | - | - | Fake Tears | Fake Tears |
| 22 | Faint Attack | Faint Attack | - | - |
| 25 | - | - | Faint Attack | Faint Attack |
| 29 | Rest | Rest | - | - |
| 31 | - | - | Rest | Rest |
| 36 | Slash | Slash | - | - |
| 37 | - | - | Slash | Slash |
| 43 | Snore | Snore | Snore | Snore |
| 49 | - | - | Thrash | Thrash |
| 50 | Thrash | Thrash | - | - |

### TM/HM

* GS/C/RS/FL: Attract, Cut, Dig, Double Team, Earthquake, Frustration, Hidden Power, Protect, Rest, Return, Roar, Rock Smash, Strength, Sunny Day, Thief, Toxic
* GS/C: Curse, Defense Curl, Dynamicpunch, Endure, Fire Punch, Fury Cutter, Headbutt, Ice Punch, Mud-Slap, Rollout, Sleep Talk, Snore, Swagger, Swift, Thunderpunch, Zap Cannon
* RS/FL: Aerial Ace, Brick Break, Bulk Up, Facade, Focus Punch, Rain Dance, Secret Power, Taunt, Torment

### Breeding

* GS/C/RS/FL: Counter, Crunch, Seismic Toss, Take Down
* C/RS/FL: Metal Claw
* GS/C: Focus Energy
* RS/FL: Fake Tears, Sleep Talk, Yawn

## Trading Cards

* Neo Discovery #65 - Teddiursa
* Skyridge #109 - Teddiursa
| Basic: Teddiursa | Stage 1: Ursaring | (No Stage 2) |
# Pokémon/Pokédex/Terapagos
## Description

A turtle like pokémon.

## Base Statistics

A normal type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Terapagos: fighting Moves that deal 0% of their damage to Terapagos: ghost

## Notes

Introduced in the DLC for Pokémon Scarlet and Violet.
# Pokémon/Pokédex/Tinkatink
## Description

A small humanoid Pokémon.

## Base Statistics

A Fairy and Steel type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Tinkatink: poison, fire, ground Moves that deal 50% of their damage to Tinkatink: dark, normal, grass, ice, flying, psychic, rock, dragon, fairy Moves that deal 25% of their damage to Tinkatink: bug Moves that deal 0% of their damage to Tinkatink: dragon, poison

## How to Evolve

Evolves to Tinkatuff.

## Notes

Introduced in Pokémon Scarlet and Violet.
# Pokémon/Pokédex/Toedscool
## Description

A Pokémon resembling Tentacool in appearance.

## Base Statistics

A ground and grass type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Toedscool: ice, fire, flying, bug Moves that deal 50% of their damage to Toedscool: rock, electric, ground Moves that deal 0% of their damage to Toedscool: electric

## How to Evolve

Evolves into Toedscruel.

## Notes

Introduced in Pokémon Scarlet and Violet.
# Pokémon/Pokédex/Tinkaton
## Description

A humanoid Pokémon.

## Base Statistics

A Fairy and Steel type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Tinkaton: poison, fire, ground Moves that deal 50% of their damage to Tinkaton: dark, normal, grass, ice, flying, psychic, rock, dragon, fairy Moves that deal 25% of their damage to Tinkaton: bug Moves that deal 0% of their damage to Tinkaton: dragon, poison

## How to Evolve

Evolves from Tinkatuff.

## Notes

Introduced in Pokémon Scarlet and Violet.
# Pokémon/Pokédex/Tinkatuff
## Description

A humanoid Pokémon.

## Base Statistics

A Fairy and Steel type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Tinkatuff: poison, fire, ground Moves that deal 50% of their damage to Tinkatuff: dark, normal, grass, ice, flying, psychic, rock, dragon, fairy Moves that deal 25% of their damage to Tinkatuff: bug Moves that deal 0% of their damage to Tinkatuff: dragon, poison

## How to Evolve

Evolves from Tinkatink and into Tinkaton.

## Notes

Introduced in Pokémon Scarlet and Violet.
# Pokémon/Pokédex/Toedscruel
## Description

A Pokémon resembling Tentacruel in appearance.

## Base Statistics

A ground and grass type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Toedscruel: ice, fire, flying, bug Moves that deal 50% of their damage to Toedscruel: rock, electric, ground Moves that deal 0% of their damage to Toedscruel: electric

## How to Evolve

Evolves from Toedscool.

## Notes

Introduced in Pokémon Scarlet and Violet.
# Ordinary Differential Equations/Linear Equations
## Linear Equations and Linear Operators

A general linear equation is of the form
$P_{0}(x)y^{(n)}+P_{1}(x)y^{(n-1)}+...+P_{n}y=Q(x)$,
where we will assume that the coefficient functions $P_{i}(x)$ and Q(x) are continuous functions in an interval [a,b], and that $P_{0}(x)\neq 0$ for all $x\in [a,b]$. The existence theorem proves that a unique solution exists that passes through the point $(x_{0},y_{0})$ where $x\in [a,b]$, with continuous derivatives up to the n-1 order, and satisfies initial conditions for each of those derivatives at $x_{0}$.
One can also write this as
$L(y)=(P_{0}{\frac {d^{n}}{dx^{n}}}+P_{1}{\frac {d^{n-1}}{dx^{n-1}}}+...+P_{n})y=Q(x)$
where L is called a linear differential operator of order n.
A differential equation of the form L(y)=0 with the same linear differential operator as above is called a homogeneous equation corresponding to the above equation, and the reduced equation of the above equation.
We will now prove some properties about the linear differential operator.
The linear differential operator:
$L(C_{1}y_{1}+C_{2}y_{2})=C_{1}L(y_{1})+C_{2}L(y_{2})$ which is true because differentiation is linear. Thus, we can make the two following statements:
* If $y_{1}$ and $y_{2}$ are two solutions of the homogeneous equation, then $C_{1}y_{1}+C_{2}y_{2}$ is also a solution.
* If y is a solution to the homogeneous equation L(y)=0, and $y_{0}$ is a solution to the equation L(y)=Q(x), then $y+y_{0}$ is also a solution to the equation L(y)=Q(x).

## Wronskian

Let L(y)=0 be a homogeneous equation of degree n, and let $y_{1},y_{2},...,y_{n}$ be linearly independent solutions of this equation.
The general solution is then $y=C_{1}y_{1}+C_{2}y_{2}+...+C_{n}y_{n}$.
Suppose instead that the solutions are not linearly independent. Then there exists values for $C_{1},C_{2},...,C_{n}$ not all zero such that $C_{1}y_{1}+C_{2}y_{2}+...+C_{n}y_{n}$=0.
Then the following equations also hold true:
$C_{1}y_{1}'+C_{2}y_{2}'+...+C_{n}y_{n}'=0$ $C_{1}y_{1}''+C_{2}y_{2}''+...+C_{n}y_{n}''=0$ ... $C_{1}y_{1}^{(n-1)}+C_{2}y_{2}^{(n-1)}+...+C_{n}y_{n}^{(n-1)}=0$
When there is to be a non-trivial solution to this system of homogeneous linear equations, the column vectors corresponding to each coefficient are linearly dependent. This is equivalent to saying that the following determinant, called the Wronskian is 0:
${\begin{Vmatrix}y_{1}&y_{2}&...&y_{n}\\y_{1}'&y_{2}'&...&y_{n}'\\y_{1}''&y_{2}''&...&y_{n}''\\...&...&...&...\\y_{1}^{(n-1)}&y_{2}^{(n-1)}&...&y_{n}^{(n-1)}\\\end{Vmatrix}}=0$
Thus, if the solutions are dependent, then their Wronskian is equal to 0, and conversely, and conversely if the Wronskian is equal to 0, then the columns of that matrix must be linearly dependent, indicating that the solutions are linearly dependent.
# Ordinary Differential Equations/Nonhomogeneous second order equations:Method of undetermined coefficients

Consider a differencial equation of the form
$y''+p(t)y'+q(t)y=g(t)$
Clerarly, this is not homogeneous, as $g(t)\neq 0$.
So, to solve this, we first proceeed as normal, but assume that the equation is homogeneous; set $g(t)=0$for now. Then the first part of the solution pans like $y(t)=c_{1}e^{r_{1}t}+c_{2}e^{r_{2}t}.$.
Now we need to find the particular integral. To do this, make an appropriate substitution that relates to what $g(t)$ is. For instance, if $g(t)=e^{2x}$, then take substitution $Ae^{2x}$. As $y''$ and $y'$ are multiples of $y$ in this case, you'll simply get a linear equation in $A$. Then just plug the value of $A$ in the equation.
Hence the solution is
y = general solution + particular integral.
There is one important caveat which you should be aware though. In the previous example for instance, if the general solution already had $e^{2x}$, the substitution cannot be $Ae^{2x}$, as the particular integral cannot be equal to the general solution. In such cases, you need to take the substitution as $Axe^{2x}$.

## Example

Solve the differential equation
${\frac {d^{2}y}{dx^{2}}}+{\frac {2dy}{dx}}+2y=4+e^{-2x}$ Given that $y(0)=4,y'(0)=-1$

### Solution

Take $y=e^{mx}$. Then
$(d^{2}y)/(dx^{2})+2dy/dx+2y\rightarrow (m+1)^{2}+1=0\rightarrow m+1=\pm i\rightarrow m=-1\pm i$
Hence the general form of the equation becomes
$y=e^{-x}\left(P\cos {x}+Q\sin {x}\right)$ Now, the particular integral has to be found. To do so, we consider RHS: $4+{2e}^{-2x}$. The substation then becomes $A+Be^{-2x}$. Then $y^{\prime }=-2Be^{-2x}$ and $y^{\prime \prime }=4Be^{-2x}$. Then the equation reduces to $4B-4B+2\left(A+Be^{-2x}\right)=4+2e^{-2x}\rightarrow 2A+2Be^{-2x}=4+2e^{-2x}$. Hence $A=2,B=1$. The equation is now
$y=e^{-x}\left(P\cos {x}+Q\sin {x}\right)+2+e^{-2x}$
$y\left(0\right)=4.$ Then $4=P+2+1\rightarrow P=1.$ $y^{\prime }\left(0\right)=-1$. Then $-e^{-x}\left(P\cos {x}+Q\sin {x}\right)+e^{-x}\left(Q\cos {x}-P\sin {x}\right)-2e^{-2x}=-1=>\ Q-P-2=-1\rightarrow Q-P=1\rightarrow Q=2.$
Hence the final equation is $y=e^{-x}\left(\cos {x}+2\sin {x}\right)+2+e^{-2x}$
# Ordinary Differential Equations/Non Homogenous 4
### Solve

1. $y''-y=e^{-x},x\in \mathbb {R} ,y(0)=y'(0)=0$
Answer: $y(x)={\frac {1}{4}}e^{x}-{\frac {1}{4}}e^{-x}-{\frac {1}{2}}xe^{-x}$

### Find Particular Integral

1. $y''-7y+12y=24e^{x}$
Answer: $y_{p}(x)=4e^{-x}$
2. $y''+4y'+4y=e^{-2x}$
Answer: $y_{p}(x)={\frac {1}{2}}x^{2}e^{-2x}$
# Ordinary Differential Equations/Legendre Equation

In mathematics, Legendre's differential equation is
    ${d \over dx}\left[(1-x^{2}){d \over dx}P_{n}(x)\right]+n(n+1)P_{n}(x)=0.$
They are named after Adrien-Marie Legendre. This ordinary differential equation is frequently encountered in physics and other technical fields. In particular, it occurs when solving Laplace's equation (and related partial differential equations) in spherical coordinates.
The Legendre differential equation may be solved using the standard power series method. The equation has regular singular points at $x=\pm 1$ so, in general, a series solution about the origin will only converge for $\left\vert x\right\vert <1$. When n is an integer, the solution $P_{n}\left(x\right)$ that is regular at $x=1$ is also regular at $x=-1$, and the series for this solution terminates (i.e. is a polynomial).
The solutions for $n=0,1,2\dots$ (with the normalization $P_{n}\left(1\right)=1$) form a polynomial sequence of orthogonal polynomials called the Legendre polynomials. Each Legendre polynomial $P_{n}\left(x\right)$ is an nth-degree polynomial. It may be expressed using Rodrigues' formula:
    $P_{n}(x)={1 \over 2^{n}n!}{d^{n} \over dx^{n}}\left[(x^{2}-1)^{n}\right].$
# Ordinary Differential Equations/Linear Systems

A system of differential equations is a collection of two or more differential equations, which each ODE may depend upon the other unknown function.
For example consider the equations:
    ${\begin{cases}x'(t)=2x(t)+y(t)\\y'(t)=3y(t)\end{cases}}$
In this case the equation for differential equation for $x'(t)$ depends on both $x(t)$ and $y(t)$. In principle we could also allow $y'(t)$ to depend on both $x$ and $y$, but it is not necessary.
Notice in some cases we find a solution for a system of ODE's. For example in the case above, because $y'$ doesn't depend on $x$ we can solve the second equation (by separating variables or using an integrating factor) to get that $y=C_{2}e^{3t}$. Since there will be a second constant when we solve the first ODE, we choose to call the constant here $C_{2}$. Now we can plug this into the first equation to get that: $x'=2x+C_{2}e^{3t}$. We can solve this equation by using an integrating factor to get that:
    ${\begin{cases}x(t)=C_{1}e^{2t}+C_{2}e^{3t}\\y(t)=C_{2}e^{3t}\end{cases}}$
In other cases a clever change of variables allows one to separate the two ODE's. Consider the system
    ${\begin{cases}x_{1}'(t)=4x_{1}(t)+2x_{2}(t)\\x_{2}'(t)=2x_{1}(t)+4x_{2}(t)\end{cases}}$.
If we let $y_{1}=x_{1}+x_{2}$ and $y_{2}=x_{1}-x_{2}$. Then we find that
    ${\begin{cases}y_{1}'(t)=6y_{1}(t)\\y_{2}'(t)=2y_{2}(t)\end{cases}}$
and each of these are easy to solve: $y_{1}=C_{1}e^{6t}$ and $y_{2}=C_{2}e^{2t}$. And so we find $x_{1}=C_{1}e^{6t}+C_{2}e^{2t}$ and $x_{1}=C_{1}e^{6t}-C_{2}e^{2t}$. It turns out to be helpful with systems to work with vectors and matrices so if we introduce $\textstyle {\vec {x}}(t)={\begin{pmatrix}x_{1}(t)\\x_{2}(t)\end{pmatrix}}.$ Then the above system can be re-written as:
    ${\frac {d}{dt}}{\vec {x}}(t)={\begin{pmatrix}4&2\\2&4\end{pmatrix}}{\vec {x}}(t).$
And we have solutions ${\vec {x}}_{1}(t)=C_{1}e^{6t}{\begin{pmatrix}1\\1\end{pmatrix}}$ and ${\vec {x}}_{2}(t)=C_{2}e^{2t}{\begin{pmatrix}1\\-1\end{pmatrix}}$
Notice that the solutions we found were of the for $e^{\lambda t}{\vec {\xi }}$ for some constant vector ${\vec {\xi }}$. Using this as motivation we will investigate the question, when does ${\vec {x}}(t)=e^{\lambda t}{\vec {\xi }}$ solve the system:
    ${\frac {d}{dt}}{\vec {x}}(t)=A{\vec {x}}(t).$
for some constant matrix $A$.
By substituting into the equation we see that:
${\begin{aligned}{\frac {d}{dt}}(e^{\lambda t}{\vec {\xi }})&=A(e^{\lambda t}{\vec {\xi }})\\\lambda e^{\lambda t}{\vec {\xi }}&=e^{\lambda t}A{\vec {\xi }}\\e^{\lambda t}(A-\lambda I){\vec {\xi }}&={\vec {0}}.\end{aligned}}$
Since $e^{\lambda t}\neq 0$, the only way for the left hand side to be ${\vec {0}}$ is if $\lambda$ is an eigenvalue and ${\vec {\xi }}$ is a corresponding eigenvector.
This is not quite the end of the story. When the matrix is real we shall consider the following cases:
# Ordinary Differential Equations/Non Homogenous 3
### Solve

* $y''-y=e^{-x},x\in \mathbb {R} ,y(0)=y'(0)=0$

### Find Particular Integral

* $y''-7y+12y=24e^{x}$
* $y''+4y'+4y=e^{-2x}$
# Pinyin/Androgen

See also
# Pinyin/Anger

See also
# Pinyin/And

See also
# Pinyin/Annualized

See also
# Pinyin/Announce

See also
# Pinyin/Annual

Search annual
# Pinyin/Another
## Adjective

* another: other one
** lihngyi: lihngwaih 1'g
# Pinyin/Animal

Search Pinyin animal
Animals are eukaryotic organisms with many cells. They do not use light to get energy and grow, as plants do. The study of animals is called zoology. Animals use different ways to get energy from other living things. They usually eat other living things, but some are parasites, or have photosynthetic protists as symbionts.
dòngwù shì yǒu hěnduō'g xìbāo d zhēnhéxìbāo shēngwù. Tāmen bù xiàng zhíwù yòng guāng dédào néngliàng shēngzhǎng. Dòngwù d yánjiū jiàozuò dòngwùxué. Dòngwù yòng bùtóng fāngfǎ cóng qítā shēngwù dédào néngliàng. Tāmen tōngcháng chī qítā shēngwù, dàn yǒuxiē shì jìshēngchóng, huòzhě yǒu guānghézuòyòng d yuánshēngshēngwù rú gòngshēngshēngwù.
# Pinyin/Anniversary

See also
# Practical Electronics/Breadboard

The breadboard (also called a protoboard) is used to create circuits without soldering components together. The pins are connected vertically along the grey and red lines and horizontally in the sections in between. Note that they do not connect across the gap in the center.

## Further reading

* Practical Electronics/Plugins
* mechatronics design wiki: "Using Solderless Breadboard"
# Practical Electronics/Binary
## Binary Number

Binary numbers are numbers in base two which consists of two digit 0 and 1 . A series of 0's and 1's can be formed to represent info
For example number from 0 to 9 can be expressed as binary numbers of four bit as shown
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |

## Binary Coding

Since in binary number system there are only two digits 0 and 1 called a Bit . So 1-bit binary number refers to number of 1 digit either 0 or 1 . 2-bit binary number refers to number of 2 digit namely 00, 01, 10, 11 and there are 4 of such numbers which equivalent to 2$^2$. Hence, there are 2$^n$ binary numbers of n bits
The process of using binary numbers to represent info is called Binary Coding
For example with 1-bit binary number 0 and 1 can be used to represent number 0 and 1 in our system .
With 2-bit binary number can be used to represent number 0 to 3 in our system as follow
    00 represents 0
    01 represents 1
    10 represents 2
    11 represents 3
With digit 0 and 1 we have three bit binary numbers of 000, 001, 010, 011, 100, 101, 110, 111 which equivalent to 0, 1, 2, 3, 4, 5, 6, 7
# Practical Electronics/Bipolar Transistors/PNP Transistor
## PNP Transistor

A PNP transistor is made by joining one Negative Typed Semiconductor in between two Positive Typed Semiconductors.
The symbol for a PNP Transistor:

## Transistor's Rectifier

A PNP Transistor only allows half of a negative cycle of a voltage or signal wave to pass and grounds any positive cycle of a voltage or signal wave.
# Practical Electronics/Bipolar Transistors/NPN Transistor/Transistor circuit

    ${\frac {v_{o}}{v_{i}}}=({\frac {R_{2}}{R_{2}+R_{3}}})({\frac {R_{4}}{R_{3}}})$

## Electronics switch

When $R_{3}=R_{4}$, Transistor operates as Electronics switch
    ${\frac {v_{o}}{v_{i}}}={\frac {R_{2}}{R_{2}+R_{3}}}$
    ${\frac {v_{o}}{v_{i}}}=0$ . $R_{2}=0$
    ${\frac {v_{o}}{v_{i}}}=1$ . $R_{1}=0$

## Electronics amplifier

When $R_{1}=0$, Transistor operates as Electronics amplifier
    ${\frac {v_{o}}{v_{i}}}=A$ . $R_{4}=AR_{3}$
    $v_{o}=Av_{i}$

## Transistor's Rectifier

A PNP Transistor only allows half of a negative cycle of a voltage or signal wave to pass and grounds any positive cycle of a voltage or signal wave.