y2+y=x by variation of parameters?

Answer 1

You probably meant y’’ + y = x

This is just a second-order linear ordinary differential equation with solution

y = Asin x + Bcos x + x

Using the variation of parameters method would be using a sledge hammer

to crush a walnut; however a demonstration of that method with a similar example can be found here.

https://duckduckgo.com/?q=variation+of+parameters+...