2.623   ODE No. 623

\[ y'(x)=\frac {x^2}{x^{3/2}+y(x)} \] Mathematica : cpu = 0.203697 (sec), leaf count = 77


\[\text {Solve}\left [6 \sqrt {33} \tanh ^{-1}\left (\frac {7 x^{3/2}+3 y(x)}{\sqrt {33} \left (x^{3/2}+y(x)\right )}\right )+44 c_1=33 \left (\log \left (-\frac {3 y(x)}{2 x^{3/2}}-\frac {3 y(x)^2}{2 x^3}+1\right )+3 \log (x)\right ),y(x)\right ]\] Maple : cpu = 0.255 (sec), leaf count = 49


\[\ln \left (3 x^{\frac {3}{2}} y \relax (x )-2 x^{3}+3 y \relax (x )^{2}\right )-\frac {2 \sqrt {33}\, \arctanh \left (\frac {\left (x^{\frac {3}{2}}+2 y \relax (x )\right ) \sqrt {33}}{11 x^{\frac {3}{2}}}\right )}{11}-c_{1} = 0\]