- #1

Danny B

- 5

- 0

## Homework Statement

Consider the ODE:

y''+p(x)y'+q(x)y=g(x)

It is given that the functions y=x[itex]^{2}[/itex], y=x and y[itex]\equiv[/itex]1

are solutions of the equation.

Find the general solution of the equation.

## Homework Equations

## The Attempt at a Solution

Well, given the three solutions, and taking into account that they are mutually linearly independent, I would say that any couple of these functions will give me a set that forms the general solution.

If i take y=x and y[itex]\equiv[/itex]1, I get the general solution:

y(x)=c1+c2*x

Now, I know that x[itex]^{2}[/itex] is also a solution, but it can't be derived from the general solution, so obviously I'm doing something wrong.

I also thought of the possibility that y=1 is a singular solution and the general solution is:

y(x)=c1*x+c2*x^2

does this makes sense?

This is a question from my midterm and i still can't figure it out. So... help?