2.851   ODE No. 851

\[ y'(x)=\frac {a^3 x^3+3 a^2 b x^2 y(x)+a^2 b x^2+3 a b^2 x y(x)^2+2 a b^2 x y(x)+b^3 y(x)^3+b^3 y(x)^2+b^3}{b^3} \] Mathematica : cpu = 0.366508 (sec), leaf count = 145


\[\text {Solve}\left [-\frac {1}{3} (27 a+29 b)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (27 a+29 b)^{2/3}-3 \text {$\#$1} b^{2/3}+(27 a+29 b)^{2/3}\& ,\frac {\log \left (\frac {\frac {3 a x+b}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right )}{b^{2/3}-\text {$\#$1}^2 (27 a+29 b)^{2/3}}\& \right ]=\frac {1}{9} x \left (\frac {27 a+29 b}{b}\right )^{2/3}+c_1,y(x)\right ]\] Maple : cpu = 0.054 (sec), leaf count = 42


\[y \relax (x ) = \frac {\RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} b +\textit {\_a}^{2} b +a +b}d \textit {\_a} \right ) b -x +c_{1}\right ) b -a x}{b}\]