ODE No. 230

\[ a y(x) y'(x)+b y(x)^2+f(x)=0 \] Mathematica : cpu = 0.173082 (sec), leaf count = 98

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

\[\left \{\left \{y(x)\to -e^{-\frac {b x}{a}} \sqrt {2 \int _1^x-\frac {e^{\frac {2 b K[1]}{a}} f(K[1])}{a}dK[1]+c_1}\right \},\left \{y(x)\to e^{-\frac {b x}{a}} \sqrt {2 \int _1^x-\frac {e^{\frac {2 b K[1]}{a}} f(K[1])}{a}dK[1]+c_1}\right \}\right \}\] Maple : cpu = 0.053 (sec), leaf count = 100

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

\[y \left (x \right ) = \frac {{\mathrm e}^{-\frac {2 b x}{a}} \sqrt {{\mathrm e}^{\frac {2 b x}{a}} a \left (c_{1} a -2 \left (\int {\mathrm e}^{\frac {2 b x}{a}} f \left (x \right )d x \right )\right )}}{a}\]