(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I must solve [itex](1-x)y''+xy'-y=(1-x)^2[/itex] 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 [itex]y''+y' \left ( \frac{x}{1-x} \right )-y \left ( \frac{1}{1-x} \right ) =1-x[/itex].

Any tip will be appreciated, as usual.

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# Homework Help: Second order DE

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