Hello,

Given is $\displaystyle xy^{'}- (x+1)y=x^2-x^3$

Before I start I multiply by $\displaystyle \frac{1}{x}$

Then I get $\displaystyle y'-\frac{x+1}{x}y=\frac{x^2-x^3}{x}$

First I will find the solution of the homogeneous DV $\displaystyle y'-\frac{x+1}{x}y=0$

I can solove this easely $\displaystyle \int dy=\int\frac{x+1}{x}$ and I get $\displaystyle y=x+\ln x+k(x)$

I deveritate this and I get $\displaystyle y'=1+\frac{1}{x}+k'(x)$ and now I need to put in but then I miss ???

Who can help me? Greets.