2.748   ODE No. 748

\[ y'(x)=\frac {y(x) (y(x)+x)}{x \left (y(x)^3+x\right )} \] Mathematica : cpu = 0.269172 (sec), leaf count = 285


\[\left \{\left \{y(x)\to \frac {2 \sqrt [3]{2} (\log (x)+c_1)}{\sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}+\frac {\sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}{3 \sqrt [3]{2}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{2} \left (1+i \sqrt {3}\right ) (\log (x)+c_1)}{\sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}{6 \sqrt [3]{2}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{2} \left (1-i \sqrt {3}\right ) (\log (x)+c_1)}{\sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{54 x+\sqrt {2916 x^2-864 (\log (x)+c_1){}^3}}}{6 \sqrt [3]{2}}\right \}\right \}\] Maple : cpu = 0.123 (sec), leaf count = 404


\[y \relax (x ) = \frac {\left (27 x +3 \sqrt {-24 c_{1}^{3}-72 c_{1}^{2} \ln \relax (x )-72 c_{1} \ln \relax (x )^{2}-24 \ln \relax (x )^{3}+81 x^{2}}\right )^{\frac {2}{3}}+6 \ln \relax (x )+6 c_{1}}{3 \left (27 x +3 \sqrt {-24 c_{1}^{3}-72 c_{1}^{2} \ln \relax (x )-72 c_{1} \ln \relax (x )^{2}-24 \ln \relax (x )^{3}+81 x^{2}}\right )^{\frac {1}{3}}}\]