2.268   ODE No. 268

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

\[ f(x) y(x) y'(x)+g(x) y(x)^2+h(x)=0 \] Mathematica : cpu = 0.198925 (sec), leaf count = 146

\[\left \{\left \{y(x)\to -\exp \left (\int _1^x-\frac {g(K[1])}{f(K[1])}dK[1]\right ) \sqrt {2 \int _1^x-\frac {\exp \left (-2 \int _1^{K[2]}-\frac {g(K[1])}{f(K[1])}dK[1]\right ) h(K[2])}{f(K[2])}dK[2]+c_1}\right \},\left \{y(x)\to \exp \left (\int _1^x-\frac {g(K[1])}{f(K[1])}dK[1]\right ) \sqrt {2 \int _1^x-\frac {\exp \left (-2 \int _1^{K[2]}-\frac {g(K[1])}{f(K[1])}dK[1]\right ) h(K[2])}{f(K[2])}dK[2]+c_1}\right \}\right \}\] Maple : cpu = 0.09 (sec), leaf count = 118

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