2.141   ODE No. 141

\[ a x y(x)+b+x^2 \left (y'(x)+y(x)^2\right )=0 \] Mathematica : cpu = 0.131508 (sec), leaf count = 67


\[\left \{\left \{y(x)\to -\frac {a}{2 x}-\frac {-1+\sqrt {a^2-2 a-4 b+1} \left (-1+\frac {2 c_1}{x^{\sqrt {a^2-2 a-4 b+1}}+c_1}\right )}{2 x}\right \}\right \}\] Maple : cpu = 0.059 (sec), leaf count = 51


\[y \relax (x ) = \frac {-\tanh \left (\frac {\sqrt {a^{2}-2 a -4 b +1}\, \left (-\ln \relax (x )+c_{1}\right )}{2}\right ) \sqrt {a^{2}-2 a -4 b +1}-a +1}{2 x}\]