8.51   ODE No. 1641

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+h\left(y\left(x\right)\right){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+g\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=0}}$$

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

Mathematica: cpu = 2.378802 (sec), leaf count = 57 $$\left\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}{e}^{-{\int }_1^{K[4]}-h(K[1])dK[1]}dK[4]\mathrm{\&}][{\int }_1^x{c}_1(-e^{-{\int }_1^{K[5]}g(K[2])dK[2]})dK[5]+c_2]\}\right\}$$

Maple: cpu = 0.032 (sec), leaf count = 29 $$\{{\int }^{y\left(x\right)}{\mathrm{e}}^{\int h\left(\mathit{\_}\mathit{b}\right)\mathrm{d}\mathit{\_}\mathit{b}}d\mathit{\_}\mathit{b}-\mathit{\_}\mathit{C}\mathit{1}\int {\mathrm{e}}^{-\int g\left(x\right)\mathrm{d}x}\mathrm{d}x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$