How do I show, that (x, 1+x²) is a fundamental set for the equation

(1-x²)*(d²y/dx²)+2x*(dy/dx)-2y=0

and state an open interval where I belongs to R on which y=cx+d(1+x²) is the unique solution to the equation (c and d being arbitrary constants)

and

how do I find the general solution to

(d^4y/dx^4)+8(d²y/dx²)-9y=e^x-sin(x)

Thanks for your time