2.623   ODE No. 623

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

\[ y'(x)=\frac {x^2}{x^{3/2}+y(x)} \] Mathematica : cpu = 0.137942 (sec), leaf count = 77

\[\text {Solve}\left [6 \sqrt {33} \tanh ^{-1}\left (\frac {7 x^{3/2}+3 y(x)}{\sqrt {33} \left (x^{3/2}+y(x)\right )}\right )+44 c_1=33 \left (\log \left (-\frac {3 y(x)^2}{2 x^3}-\frac {3 y(x)}{2 x^{3/2}}+1\right )+3 \log (x)\right ),y(x)\right ]\] Maple : cpu = 0.85 (sec), leaf count = 49

\[ \left \{ \ln \left ( 3\,{x}^{3/2}y \left ( x \right ) -2\,{x}^{3}+3\, \left ( y \left ( x \right ) \right ) ^{2} \right ) -{\frac {2\,\sqrt {33}}{11}{\it Artanh} \left ( {\frac {\sqrt {33}}{11} \left ( {x}^{{\frac {3}{2}}}+2\,y \left ( x \right ) \right ) {x}^{-{\frac {3}{2}}}} \right ) }-{\it \_C1}=0 \right \} \]