#### 2.748   ODE No. 748

$y'(x)=\frac {y(x) (y(x)+x)}{x \left (y(x)^3+x\right )}$ Mathematica : cpu = 0.292097 (sec), leaf count = 285

$\left \{\left \{y(x)\to \frac {2 \sqrt [3]{2} (c_1+\log (x))}{\sqrt [3]{\sqrt {2916 x^2-864 (c_1+\log (x)){}^3}+54 x}}+\frac {\sqrt [3]{\sqrt {2916 x^2-864 (c_1+\log (x)){}^3}+54 x}}{3 \sqrt [3]{2}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{2} \left (1+i \sqrt {3}\right ) (c_1+\log (x))}{\sqrt [3]{\sqrt {2916 x^2-864 (c_1+\log (x)){}^3}+54 x}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {2916 x^2-864 (c_1+\log (x)){}^3}+54 x}}{6 \sqrt [3]{2}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{2} \left (1-i \sqrt {3}\right ) (c_1+\log (x))}{\sqrt [3]{\sqrt {2916 x^2-864 (c_1+\log (x)){}^3}+54 x}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {2916 x^2-864 (c_1+\log (x)){}^3}+54 x}}{6 \sqrt [3]{2}}\right \}\right \}$ Maple : cpu = 0.082 (sec), leaf count = 404

$\left \{ y \left ( x \right ) ={\frac {1}{6} \left ( \left ( i \left ( 27\,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,{{\it \_C1}}^{2}\ln \left ( x \right ) -72\,{\it \_C1}\, \left ( \ln \left ( x \right ) \right ) ^{2}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}} \right ) ^{{\frac {2}{3}}}-6\,i{\it \_C1}-6\,i\ln \left ( x \right ) \right ) \sqrt {3}- \left ( 27\,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,{{\it \_C1}}^{2}\ln \left ( x \right ) -72\,{\it \_C1}\, \left ( \ln \left ( x \right ) \right ) ^{2}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}} \right ) ^{{\frac {2}{3}}}-6\,{\it \_C1}-6\,\ln \left ( x \right ) \right ) {\frac {1}{\sqrt [3]{27\,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,{{\it \_C1}}^{2}\ln \left ( x \right ) -72\,{\it \_C1}\, \left ( \ln \left ( x \right ) \right ) ^{2}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}}},y \left ( x \right ) =-{\frac {1}{6} \left ( \left ( i \left ( 27\,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,{{\it \_C1}}^{2}\ln \left ( x \right ) -72\,{\it \_C1}\, \left ( \ln \left ( x \right ) \right ) ^{2}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}} \right ) ^{{\frac {2}{3}}}-6\,i{\it \_C1}-6\,i\ln \left ( x \right ) \right ) \sqrt {3}+ \left ( 27\,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,{{\it \_C1}}^{2}\ln \left ( x \right ) -72\,{\it \_C1}\, \left ( \ln \left ( x \right ) \right ) ^{2}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}} \right ) ^{{\frac {2}{3}}}+6\,{\it \_C1}+6\,\ln \left ( x \right ) \right ) {\frac {1}{\sqrt [3]{27\,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,{{\it \_C1}}^{2}\ln \left ( x \right ) -72\,{\it \_C1}\, \left ( \ln \left ( x \right ) \right ) ^{2}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}}},y \left ( x \right ) ={\frac {1}{3} \left ( \left ( 27\,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,{{\it \_C1}}^{2}\ln \left ( x \right ) -72\,{\it \_C1}\, \left ( \ln \left ( x \right ) \right ) ^{2}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}} \right ) ^{{\frac {2}{3}}}+6\,\ln \left ( x \right ) +6\,{\it \_C1} \right ) {\frac {1}{\sqrt [3]{27\,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,{{\it \_C1}}^{2}\ln \left ( x \right ) -72\,{\it \_C1}\, \left ( \ln \left ( x \right ) \right ) ^{2}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}}} \right \}$