2.398   ODE No. 398

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

\[ y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0 \] Mathematica : cpu = 1.24727 (sec), leaf count = 175

\[\left \{\text {Solve}\left [\frac {1}{6} \left (-6 c_1+\frac {\left (x^2-4 \sqrt [3]{y(x)}\right )^{3/2} y(x)^2 \left (6 \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}+x\right )-\log (y(x))\right )}{\left (\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}\right )^{3/2}}+\log (y(x))\right )=0,y(x)\right ],\text {Solve}\left [\frac {1}{6} \left (-6 c_1+\frac {\left (x^2-4 \sqrt [3]{y(x)}\right )^{3/2} y(x)^2 \left (\log (y(x))-6 \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}+x\right )\right )}{\left (\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}\right )^{3/2}}+\log (y(x))\right )=0,y(x)\right ]\right \}\]

Maple : cpu = 2.454 (sec), leaf count = 138

\[ \left \{ \ln \left ( x \right ) +{\frac {1}{6}\ln \left ( {\frac {y \left ( x \right ) }{{x}^{6}}} \right ) }-{\frac {1}{6}\ln \left ( 4\,\sqrt [3]{{\frac {y \left ( x \right ) }{{x}^{6}}}}-1 \right ) }-{1\sqrt {-4\, \left ( {\frac {y \left ( x \right ) }{{x}^{6}}} \right ) ^{5/3}+ \left ( {\frac {y \left ( x \right ) }{{x}^{6}}} \right ) ^{{\frac {4}{3}}}}{\it Artanh} \left ( \sqrt {-4\,\sqrt [3]{{\frac {y \left ( x \right ) }{{x}^{6}}}}+1} \right ) \left ( {\frac {y \left ( x \right ) }{{x}^{6}}} \right ) ^{-{\frac {2}{3}}}{\frac {1}{\sqrt {-4\,\sqrt [3]{{\frac {y \left ( x \right ) }{{x}^{6}}}}+1}}}}-{\frac {1}{6}\ln \left ( 16\, \left ( {\frac {y \left ( x \right ) }{{x}^{6}}} \right ) ^{2/3}+4\,\sqrt [3]{{\frac {y \left ( x \right ) }{{x}^{6}}}}+1 \right ) }+{\frac {1}{6}\ln \left ( 64\,{\frac {y \left ( x \right ) }{{x}^{6}}}-1 \right ) }-{\it \_C1}=0,y \left ( x \right ) ={\frac {{x}^{6}}{64}} \right \} \]