2.58   ODE No. 58

\[ a \left (-\sqrt {y(x)}\right )-b x+y'(x)=0 \] Mathematica : cpu = 0.317116 (sec), leaf count = 118


\[\text {Solve}\left [\frac {a^2 \left (-\log \left (a^2 \left (\sqrt {\frac {a^2 y(x)}{b^2 x^2}}+1\right )-\frac {2 a^2 y(x)}{b x^2}\right )-\frac {2 a \tanh ^{-1}\left (\frac {a \left (1-\frac {4 b \sqrt {\frac {a^2 y(x)}{b^2 x^2}}}{a^2}\right )}{\sqrt {a^2+8 b}}\right )}{\sqrt {a^2+8 b}}\right )}{2 b}=\frac {a^2 \log (x)}{b}+c_1,y(x)\right ]\] Maple : cpu = 0.073 (sec), leaf count = 68


\[-\frac {\ln \left (\sqrt {y \relax (x )}\, a x +b \,x^{2}-2 y \relax (x )\right )}{2}+\frac {a \sqrt {y \relax (x )}\, \arctanh \left (\frac {a \sqrt {y \relax (x )}+2 b x}{\sqrt {y \relax (x ) \left (a^{2}+8 b \right )}}\right )}{\sqrt {y \relax (x ) \left (a^{2}+8 b \right )}}+c_{1} = 0\]