2.230   ODE No. 230

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


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


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