#### 2.413   ODE No. 413

$-x^2+x y'(x)^2+y(x) y'(x)=0$ Mathematica : cpu = 301.786 (sec), leaf count = 0 , timed out

\$Aborted

Maple : cpu = 0.262 (sec), leaf count = 269

$\left \{ \int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left ( -y \left ( x \right ) -\sqrt {4\,{{\it \_a}}^{3}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( \sqrt {4\,{{\it \_a}}^{3}+ \left ( y \left ( x \right ) \right ) ^{2}}+4\,y \left ( x \right ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!{1 \left ( -2+ \left ( -48\,{\it \_f}-12\,\sqrt {4\,{x}^{3}+{{\it \_f}}^{2}} \right ) \int _{{\it \_b}}^{x}\!{{{\it \_a}}^{2} \left ( \sqrt {4\,{{\it \_a}}^{3}+{{\it \_f}}^{2}}+4\,{\it \_f} \right ) ^{-2}{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{{\it \_f}}^{2}}}}}\,{\rm d}{\it \_a} \right ) \left ( \sqrt {4\,{x}^{3}+{{\it \_f}}^{2}}+4\,{\it \_f} \right ) ^{-1}}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left ( -y \left ( x \right ) +\sqrt {4\,{{\it \_a}}^{3}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( 4\,y \left ( x \right ) -\sqrt {4\,{{\it \_a}}^{3}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!{1 \left ( -2+ \left ( 48\,{\it \_f}-12\,\sqrt {4\,{x}^{3}+{{\it \_f}}^{2}} \right ) \int _{{\it \_b}}^{x}\!{{{\it \_a}}^{2} \left ( -4\,{\it \_f}+\sqrt {4\,{{\it \_a}}^{3}+{{\it \_f}}^{2}} \right ) ^{-2}{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{{\it \_f}}^{2}}}}}\,{\rm d}{\it \_a} \right ) \left ( 4\,{\it \_f}-\sqrt {4\,{x}^{3}+{{\it \_f}}^{2}} \right ) ^{-1}}{d{\it \_f}}+{\it \_C1}=0 \right \}$