Solving DE Using Variation of Parameters & Given Solution

[fluidistic]

Homework Statement

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

Homework Equations

Variation of parameters?

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.

 

[jackmell]

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

 

[fluidistic]

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

Thanks, this worked out well.