# Math Help - differential equations

1. ## differential equations

When told to show that something is a solution of a differential equation, then asked to determine the general solution, how do I do it?

2. ## Re: differential equations

It depends, to solve some types of differential equations you need an obvious solution. Can you show the differential equation you need to solve?

3. ## Re: differential equations

Unless you are given other information, there is no way to go from a given solution to the general solution.

Now, if the differential equation is linear second order equation you can use a given solution to reduce to a first order equation and solve that for a second, independent, solution and so write the general solution as a linear combination of the two solutions.

4. ## Re: differential equations

For example, show that y = x is a solution of the equation (1 - x^2)d^2y/dx^2 + (2x)dy/dx - 2y = 0

I can show that y = x is a solution, but then they ask me to find the general solution of the equation