2.729   ODE No. 729

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y'(x)=\frac {(x-y(x)) y(x)}{x \left (x-y(x)^3\right )} \] Mathematica : cpu = 0.298813 (sec), leaf count = 319

\[\left \{\left \{y(x)\to \frac {12 \sqrt [3]{2} \left (c_1-\log (x)\right )-2^{2/3} \left (2 \sqrt {\left (6 c_1-6 \log (x)\right ){}^3+729 x^2}+54 x\right ){}^{2/3}}{6 \sqrt [3]{2 \sqrt {\left (6 c_1-6 \log (x)\right ){}^3+729 x^2}+54 x}}\right \},\left \{y(x)\to \frac {2^{2/3} \left (1+i \sqrt {3}\right ) \left (2 \sqrt {\left (6 c_1-6 \log (x)\right ){}^3+729 x^2}+54 x\right ){}^{2/3}+12 i \sqrt [3]{2} \left (\sqrt {3}+i\right ) \left (c_1-\log (x)\right )}{12 \sqrt [3]{2 \sqrt {\left (6 c_1-6 \log (x)\right ){}^3+729 x^2}+54 x}}\right \},\left \{y(x)\to \frac {2^{2/3} \left (1-i \sqrt {3}\right ) \left (2 \sqrt {\left (6 c_1-6 \log (x)\right ){}^3+729 x^2}+54 x\right ){}^{2/3}-12 i \sqrt [3]{2} \left (\sqrt {3}-i\right ) \left (c_1-\log (x)\right )}{12 \sqrt [3]{2 \sqrt {\left (6 c_1-6 \log (x)\right ){}^3+729 x^2}+54 x}}\right \}\right \}\]

Maple : cpu = 0.108 (sec), leaf count = 404

\[ \left \{ 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}}}}}},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}}}}}} \right \} \]