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 = 0.291467 (sec), leaf count = 327

\[\left \{\left \{y(x)\to \frac {\sqrt [3]{2} (-6 \log (x)+6 c_1)}{3 \sqrt [3]{54 x+\sqrt {2916 x^2+4 (-6 \log (x)+6 c_1){}^3}}}-\frac {\sqrt [3]{54 x+\sqrt {2916 x^2+4 (-6 \log (x)+6 c_1){}^3}}}{3 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{54 x+\sqrt {2916 x^2+4 (-6 \log (x)+6 c_1){}^3}}}{6 \sqrt [3]{2}}-\frac {\left (1-i \sqrt {3}\right ) (-6 \log (x)+6 c_1)}{3\ 2^{2/3} \sqrt [3]{54 x+\sqrt {2916 x^2+4 (-6 \log (x)+6 c_1){}^3}}}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{54 x+\sqrt {2916 x^2+4 (-6 \log (x)+6 c_1){}^3}}}{6 \sqrt [3]{2}}-\frac {\left (1+i \sqrt {3}\right ) (-6 \log (x)+6 c_1)}{3\ 2^{2/3} \sqrt [3]{54 x+\sqrt {2916 x^2+4 (-6 \log (x)+6 c_1){}^3}}}\right \}\right \}\] Maple : cpu = 0.292 (sec), leaf count = 404

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