2.230   ODE No. 230

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ a y(x) y'(x)+b y(x)^2+f(x)=0 \] Mathematica : cpu = 0.312155 (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

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