2.623   ODE No. 623

\[ y'(x)=\frac {x^2}{x^{3/2}+y(x)} \]

✓ Mathematica : cpu = 0.147537 (sec), leaf count = 77

DSolve[Derivative[1][y][x] == x^2/(x^(3/2) + y[x]),y[x],x]
 

\[\text {Solve}\left [6 \sqrt {33} \tanh ^{-1}\left (\frac {7 x^{3/2}+3 y(x)}{\sqrt {33} \left (x^{3/2}+y(x)\right )}\right )+44 c_1=33 \left (\log \left (-\frac {3 y(x)}{2 x^{3/2}}-\frac {3 y(x)^2}{2 x^3}+1\right )+3 \log (x)\right ),y(x)\right ]\]

✓ Maple : cpu = 0.355 (sec), leaf count = 51

dsolve(diff(y(x),x) = x^2/(y(x)+x^(3/2)),y(x))
 

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