#### 2.528   ODE No. 528

$a b x+a y'(x)^2+b y(x)+y'(x)^3=0$ Mathematica : cpu = 0.623946 (sec), leaf count = 398

$\text {Solve}\left [\left \{x=c_1-\frac {-a \left (\frac {\sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}-\frac {a}{3}\right )+\frac {3}{2} \left (\frac {\sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}-\frac {a}{3}\right )^2+a^2 \log \left (\frac {\sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}+\frac {2 a}{3}\right )}{b}\right \},y(x)\right ]$ Maple : cpu = 0.068 (sec), leaf count = 86

$\left \{ y \left ( x \right ) =-ax-{\frac { \left ( {{\rm e}^{{\it RootOf} \left ( -2\,{\it \_Z}\,{a}^{2}-3\,{{\rm e}^{2\,{\it \_Z}}}+8\,a{{\rm e}^{{\it \_Z}}}+2\,{\it \_C1}\,b-5\,{a}^{2}-2\,bx \right ) }}-a \right ) ^{2}{{\rm e}^{{\it RootOf} \left ( -2\,{\it \_Z}\,{a}^{2}-3\,{{\rm e}^{2\,{\it \_Z}}}+8\,a{{\rm e}^{{\it \_Z}}}+2\,{\it \_C1}\,b-5\,{a}^{2}-2\,bx \right ) }}}{b}} \right \}$