#### 2.504   ODE No. 504

$-\left (-a+x^3+y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0$ Mathematica : cpu = 0.359774 (sec), leaf count = 51

$\left \{y(x)\to -\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{1+2 c_1} \sqrt [3]{-a+2 a c_1+2 x^3}}{\sqrt [3]{-1+2 c_1}}\right \}$ Maple : cpu = 1.09 (sec), leaf count = 247

$\left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {{x}^{6}+ \left ( -2\,{{\it \_a}}^{3}-2\,a \right ) {x}^{3}+ \left ( -{{\it \_a}}^{3}+a \right ) ^{2}}}}}\,{\rm d}{\it \_a}-{\frac {\ln \left ( x \right ) }{2}}-{\it \_C1}=0,\int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {{x}^{6}+ \left ( -2\,{{\it \_a}}^{3}-2\,a \right ) {x}^{3}+ \left ( -{{\it \_a}}^{3}+a \right ) ^{2}}}}}\,{\rm d}{\it \_a}+{\frac {\ln \left ( x \right ) }{2}}-{\it \_C1}=0,y \left ( x \right ) =\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}},y \left ( x \right ) =\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}},y \left ( x \right ) ={\frac {-1+i\sqrt {3}}{2}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}}},y \left ( x \right ) =-{\frac {1+i\sqrt {3}}{2}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}}},y \left ( x \right ) ={\frac {-1+i\sqrt {3}}{2}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}}},y \left ( x \right ) =-{\frac {1+i\sqrt {3}}{2}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}}} \right \}$