A solution to that equation will express the velocity directly in terms of time, which can easily be integrated to get the position as a function of time. There are a number of different techniques for solving differential equations.
Complicated equations require subtle techniques.
It may seem at times that the subject of differential equations is just a collection of tricks to solve specific equations. Standard Today we will just work out the solution to one differential equation, which will be applied to a number of problems. This is the first differential equation that most people see, but this first one is also the most widely-used differential equation ever solved. The next section has lots of examples of how this equation is used to model a number of situations. The rate of decay of a radioactive substance will also behave according to this model.