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

DSolve[b + a*x*y[x] + x^2*(y[x]^2 + Derivative[1][y][x]) == 0,y[x],x]
 

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

dsolve(x^2*(diff(y(x),x)+y(x)^2)+a*x*y(x)+b = 0,y(x))
 

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