#### 2.729   ODE No. 729

$y'(x)=\frac {(x-y(x)) y(x)}{x \left (x-y(x)^3\right )}$ Mathematica : cpu = 0.28227 (sec), leaf count = 327

$\left \{\left \{y(x)\to \frac {\sqrt [3]{2} (6 c_1-6 \log (x))}{3 \sqrt [3]{\sqrt {4 (6 c_1-6 \log (x)){}^3+2916 x^2}+54 x}}-\frac {\sqrt [3]{\sqrt {4 (6 c_1-6 \log (x)){}^3+2916 x^2}+54 x}}{3 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {4 (6 c_1-6 \log (x)){}^3+2916 x^2}+54 x}}{6 \sqrt [3]{2}}-\frac {\left (1-i \sqrt {3}\right ) (6 c_1-6 \log (x))}{3\ 2^{2/3} \sqrt [3]{\sqrt {4 (6 c_1-6 \log (x)){}^3+2916 x^2}+54 x}}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {4 (6 c_1-6 \log (x)){}^3+2916 x^2}+54 x}}{6 \sqrt [3]{2}}-\frac {\left (1+i \sqrt {3}\right ) (6 c_1-6 \log (x))}{3\ 2^{2/3} \sqrt [3]{\sqrt {4 (6 c_1-6 \log (x)){}^3+2916 x^2}+54 x}}\right \}\right \}$ Maple : cpu = 0.086 (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 \}$