# Help on solving non-linear 2nd Order ODE

I need help on solving the nonlinear equation: $$x^3y''(x)-y(x)y'(x)=0$$. Mathematica simply repeats the above equation in the output.

Input:

DSolve[x^3*y''[x]-y[x]*y'[x]==0,y[x],x]

• Maple performs a complicated expression which is too long to be cited here. Jan 30 '19 at 18:10
• In the book by Micheal Greenberg, the solution to this equation is y1=1 and y2=x^2; yet their linear combination 4+3x^2 is not. This is under the section: Superposition of Solutions for Homogeneous Equation (General Solution). Jan 30 '19 at 18:11