2.540   ODE No. 540

\[ 2 y(x) y'(x)^3-y(x) y'(x)^2+2 x y'(x)-x=0 \] Mathematica : cpu = 0.0369771 (sec), leaf count = 69


\[\left \{\left \{y(x)\to \frac {x}{2}+c_1\right \},\left \{y(x)\to \frac {\left (3 c_1-2 i x^{3/2}\right ){}^{2/3}}{2^{2/3}}\right \},\left \{y(x)\to \frac {\left (2 i x^{3/2}+3 c_1\right ){}^{2/3}}{2^{2/3}}\right \}\right \}\] Maple : cpu = 0.081 (sec), leaf count = 109


\[x +\frac {x c_{1}}{\left (\frac {-\sqrt {-x y \relax (x )}+y \relax (x )}{y \relax (x )}\right )^{\frac {2}{3}} \left (\frac {-x +\sqrt {-x y \relax (x )}+y \relax (x )}{y \relax (x )}\right )^{\frac {2}{3}} y \relax (x )} = 0\]