(3x-5y)dx + (x+y) dy = 0  - Page 1
Forum section: electronics / beginners

author: J4e8a16n
author_rank: Regular Contributor
timestamp: July 30, 2015, 04:18:57 pm
content: Hi,(3x-5y)dx + (x+y) dy = 0dy/dx = (5y-3x)/ (x+y)(5y-3x)/ (x+y) = 5A/ (x+y) - 3B/ (x+y)5y-3x = 5A - 3B5y-5A = 3x - 3B5(y-A) = 3(x-B)(y-A) * 5/3= x-B...............https://www.eevblog.com/forum/Smileys/default/huh.gifHave a good day,JPDaviau

author: German_EE
author_rank: Super Contributor
timestamp: July 30, 2015, 06:51:33 pm
content: And the point of this math exercise is??

author: J4e8a16n
author_rank: Regular Contributor
timestamp: July 30, 2015, 10:18:10 pm
content: Is to find what type of solution exist for this equation.This is from Shepley L Ross 4th editionIntroduction to ordinary differential equations.It is not exact.I could not found an integrating factorI have tried v=y/x methodPartial fraction does not seem to workIt does not seem Bernouilli or homogenous.I am aiming to understand Laplace Transform.I do it for my pleasure and the pleasure to calculate my circuits.Maybe it is crasy but I am doing it for tree years now. I started with trigonometry. It is good for the mind.Well, that's it.JPDaviau

author: Mechatrommer
author_rank: Super Contributor
timestamp: July 30, 2015, 10:29:14 pm
content: Quote from: German_EE on July 30, 2015, 06:51:33 pmwasting your time and mine... in one possibility... y=A, x=B...

author: onlooker
author_rank: Frequent Contributor
timestamp: July 30, 2015, 11:26:19 pm
content: A thing having no purpose may still have solutions,(y-3x)2= C(y-x)

author: Christe4nM
author_rank: Unknown
timestamp: July 31, 2015, 10:44:25 am
content: It's a differential equation. Write it in the form of dy/dx + y = x. Then solve like a first orderlineardifferential equation.Edit: tried to rewrite and solve it, but it's a non-linear differential equation. My abilities unfortunately only include linear ones with constant coefficients

author: Jope
author_rank: Regular Contributor
timestamp: July 31, 2015, 11:09:56 am
content: Solution by Wolfram Alpha:(3x-5y)dx + (x+y) dy = 0.

author: IanB
author_rank: Super Contributor
timestamp: August 01, 2015, 05:46:23 pm
content: Quote from: J4e8a16n on July 30, 2015, 10:18:10 pmAccording to Wolfram Alpha that method leads to a solution (i.e. let y(x) = x v(x) and proceed from there). However, the solution does not come out as anything simple.

author: J4e8a16n
author_rank: Regular Contributor
timestamp: August 01, 2015, 09:38:05 pm
content: dy/dx = (5y-3x / x + y) / x = > -3 + 5y/x / 1+ y/xy/x = v y = vx ==>d y /dx = d vx/dx ==>v + v' x ==> v + x*dv/dx-----v + x* dv/dx = -3 + 5y/x / 1+ y/x ==>x dv/dx = -v^2+4v -3/ 1+vdx/x = 1+v / -v^2 +4v -3 dvfrom here complete the square?I am working at it)JPD

author: IanB
author_rank: Super Contributor
timestamp: August 01, 2015, 10:22:11 pm
content: Something like this, I believe:

author: free_electron
author_rank: Super Contributor
timestamp: August 01, 2015, 10:43:46 pm
content: Quote from: J4e8a16n on July 30, 2015, 10:18:10 pmi use this :

author: free_electron
author_rank: Super Contributor
timestamp: August 01, 2015, 10:44:55 pm
content: Laplace Transformations are for beginners. Real men use a Widlar Transformations.

author: J4e8a16n
author_rank: Regular Contributor
timestamp: August 01, 2015, 11:12:57 pm
content: Quote from: IanB on August 01, 2015, 10:22:11 pmYes.

author: IanB
author_rank: Super Contributor
timestamp: August 01, 2015, 11:14:33 pm
content: Quote from: J4e8a16n on August 01, 2015, 09:38:05 pmIt looks like you got it right up that point. You might notice that ( - v^2 + 4v - 3) can be factorized...

author: J4e8a16n
author_rank: Regular Contributor
timestamp: August 01, 2015, 11:18:04 pm
content: Thanks for your support)JPD