2.58   ODE No. 58

\[ a \left (-\sqrt {y(x)}\right )-b x+y'(x)=0 \]

✓ Mathematica : cpu = 0.289538 (sec), leaf count = 119

DSolve[-(b*x) - a*Sqrt[y[x]] + Derivative[1][y][x] == 0,y[x],x]
 

\[\text {Solve}\left [\frac {a^2 \left (-\log \left (a^2 \left (\sqrt {\frac {a^2 y(x)}{b^2 x^2}}+1\right )-\frac {2 a^2 y(x)}{b x^2}\right )-\frac {2 a \tanh ^{-1}\left (\frac {a^2-4 b \sqrt {\frac {a^2 y(x)}{b^2 x^2}}}{a \sqrt {a^2+8 b}}\right )}{\sqrt {a^2+8 b}}\right )}{2 b}=\frac {a^2 \log (x)}{b}+c_1,y(x)\right ]\]

✓ Maple : cpu = 0.092 (sec), leaf count = 68

dsolve(diff(y(x),x)-a*y(x)^(1/2)-b*x = 0,y(x))
 

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