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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]
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  • $\begingroup$ Maple performs a complicated expression which is too long to be cited here. $\endgroup$
    – user64494
    Jan 30 '19 at 18:10
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    $\begingroup$ 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). $\endgroup$ Jan 30 '19 at 18:11

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