ODE No. 487

\[ -6 x^3 y'(x)+4 x^2 y(x)+y(x)^2 y'(x)^2=0 \] Mathematica : cpu = 0.418786 (sec), leaf count = 157

DSolve[4*x^2*y[x] - 6*x^3*Derivative[1][y][x] + y[x]^2*Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\text {Solve}\left [\frac {3}{4} \log (y(x))-\frac {\sqrt {9 x^6-4 x^2 y(x)^3} \tanh ^{-1}\left (\frac {3 x^2}{\sqrt {9 x^4-4 y(x)^3}}\right )}{2 x \sqrt {9 x^4-4 y(x)^3}}=c_1,y(x)\right ],\text {Solve}\left [\frac {\sqrt {9 x^6-4 x^2 y(x)^3} \tanh ^{-1}\left (\frac {3 x^2}{\sqrt {9 x^4-4 y(x)^3}}\right )}{2 x \sqrt {9 x^4-4 y(x)^3}}+\frac {3}{4} \log (y(x))=c_1,y(x)\right ]\right \}\] Maple : cpu = 0.557 (sec), leaf count = 100

dsolve(y(x)^2*diff(y(x),x)^2-6*x^3*diff(y(x),x)+4*x^2*y(x) = 0,y(x))
 

\[y \left (x \right ) = \frac {18^{\frac {1}{3}} x^{\frac {4}{3}}}{2}\]