#### 2.398   ODE No. 398

$y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0$ Mathematica : cpu = 1.28095 (sec), leaf count = 258

$\left \{\text {Solve}\left [-\frac {\left (x^2-4 \sqrt [3]{y(x)}\right )^{3/2} y(x)^2 \log (y(x))}{6 \left (\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}\right )^{3/2}}+\frac {\sqrt {\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}} \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}+x\right )}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}+\frac {1}{6} \log (y(x))=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{6} \left (\frac {\left (x^2-4 \sqrt [3]{y(x)}\right )^{3/2} y(x)^2 \log (y(x))}{\left (\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}\right )^{3/2}}+\log (y(x))\right )-\frac {\sqrt {\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}} \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}+x\right )}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}=c_1,y(x)\right ]\right \}$ Maple : cpu = 2.519 (sec), leaf count = 137

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