2.470   ODE No. 470

\[ x^3 y'(x)-x^2 y(x)+y(x) y'(x)^2=0 \] Mathematica : cpu = 0.382072 (sec), leaf count = 143


\[\left \{\text {Solve}\left [\frac {1}{2} \log (y(x))-\frac {\sqrt {x^6+4 x^2 y(x)^2} \tanh ^{-1}\left (\frac {x^2}{\sqrt {x^4+4 y(x)^2}}\right )}{2 x \sqrt {x^4+4 y(x)^2}}=c_1,y(x)\right ],\text {Solve}\left [\frac {\sqrt {x^6+4 x^2 y(x)^2} \tanh ^{-1}\left (\frac {x^2}{\sqrt {x^4+4 y(x)^2}}\right )}{2 x \sqrt {x^4+4 y(x)^2}}+\frac {1}{2} \log (y(x))=c_1,y(x)\right ]\right \}\] Maple : cpu = 0.573 (sec), leaf count = 87


\[y \relax (x ) = -\frac {i x^{2}}{2}\]