How do you solve this differential equation: (x^3)y''+(x^2)y'-xy=x?

Question

zepdrix · Answer

$$\large x^3y''+x^2y'-xy=x$$Divide through by $\large x$,$$\large x^2y''+xy'-y=1$$The complimentary solution $\large y_c$ is given by,$$\large x^2y''+xy'-y=0$$I think this part shouldn't be too difficult, it's a Cauchy Euler Equation.
Do you know how to solve those? :o

anonymous · Answer

No, we haven't gone over them yet.

zepdrix · Answer

Hmm :o

anonymous · Answer

That's ok. I was just running through some practice problems and happened upon this one, though nothing like it was taught in the lesson. So it's not critical :) Thanks for your help, though. I'm going to be logging out pretty soon.

zepdrix · Answer

ah i see c: