2.1641   ODE No. 1641

\[ g(x) y'(x)+h(y(x)) y'(x)^2+y''(x)=0 \] Mathematica : cpu = 0.0526153 (sec), leaf count = 61


\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\exp \left (-\int _1^{K[4]}-h(K[1])dK[1]\right )dK[4]\& \right ]\left [\int _1^x-\exp \left (-\int _1^{K[5]}g(K[2])dK[2]\right ) c_1dK[5]+c_2\right ]\right \}\right \}\] Maple : cpu = 0.043 (sec), leaf count = 29


\[\int _{}^{y \relax (x )}{\mathrm e}^{\int h \left (\textit {\_b} \right )d \textit {\_b}}d \textit {\_b} -c_{1} \left (\int {\mathrm e}^{-\left (\int g \relax (x )d x \right )}d x \right )-c_{2} = 0\]