2.1814   ODE No. 1814

\[ a h(y(x)) y'(x)^2+h(y(x)) y''(x)+j(y(x))=0 \] Mathematica : cpu = 0.362357 (sec), leaf count = 120


\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {e^{a K[2]}}{\sqrt {c_1+2 \int _1^{K[2]}-\frac {e^{2 a K[1]} j(K[1])}{h(K[1])}dK[1]}}dK[2]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {e^{a K[3]}}{\sqrt {c_1+2 \int _1^{K[3]}-\frac {e^{2 a K[1]} j(K[1])}{h(K[1])}dK[1]}}dK[3]\& \right ][x+c_2]\right \}\right \}\] Maple : cpu = 0.157 (sec), leaf count = 87


\[\int _{}^{y \relax (x )}\frac {h \left (\textit {\_b} \right )^{a}}{\sqrt {-2 \left (\int \frac {h \left (\textit {\_b} \right )^{2 a}}{h \left (\textit {\_b} \right )}d \textit {\_b} \right )+c_{1}}}d \textit {\_b} -x -c_{2} = 0\]