# Second order DE

1. Oct 10, 2011

### fluidistic

1. The problem statement, all variables and given/known data
I must solve $(1-x)y''+xy'-y=(1-x)^2$ knowing that y=x is a solution if the right hand side is 0. I must use this fact in order to obtain the general solution to the DE

2. Relevant equations
Variation of parameters?

3. The attempt at a solution
I'm looking at http://tutorial.math.lamar.edu/Classes/DE/VariationofParameters.aspx and I think I need to use the Variation of parameters to solve the problem.
But I'm given only one complementary solution, not the two I would need. I really don't know how to proceed then...
What I did was rewrite the DE into $y''+y' \left ( \frac{x}{1-x} \right )-y \left ( \frac{1}{1-x} \right ) =1-x$.
Any tip will be appreciated, as usual.

2. Oct 10, 2011

### jackmell

Use Reduction of Order when you have only one solution. Just let y=xv and run it through the technique.

3. Oct 10, 2011

### fluidistic

Thanks, this worked out well.