Thread: 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?

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

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.

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