8.197   ODE No. 1787

$$\boxed{{\displaystyle 2y\left(x\right)(1-y\left(x\right))\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-(1-3y\left(x\right)){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+h\left(y\left(x\right)\right)=0}}$$

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

Mathematica: cpu = 36.216099 (sec), leaf count = 166 $$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}-\frac{1}{(K[2]-1)\sqrt{K[2]}\sqrt{2{\int }_1^{K[2]}\frac{h(K[1])e^{-2(\log (1-K[1])+\frac{1}{2}\log (K[1]))}}{2(K[1]-1)K[1]}dK[1]+c_1}}dK[2]\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{(K[3]-1)\sqrt{K[3]}\sqrt{2{\int }_1^{K[3]}\frac{h(K[1])e^{-2(\log (1-K[1])+\frac{1}{2}\log (K[1]))}}{2(K[1]-1)K[1]}dK[1]+c_1}}dK[3]\mathrm{\&}][c_2+x]\}\}$$

Maple: cpu = 0.187 (sec), leaf count = 84 $$\{{\int }^{y\left(x\right)}\frac{1}{\mathit{\_}\mathit{b}-1}\frac{1}{\sqrt{\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{{\mathit{\_}\mathit{b}}^2{(\mathit{\_}\mathit{b}-1)}^3}\mathrm{d}\mathit{\_}\mathit{b}\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{b}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\mathit{\_}\mathit{b}-1}\frac{1}{\sqrt{\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{{\mathit{\_}\mathit{b}}^2{(\mathit{\_}\mathit{b}-1)}^3}\mathrm{d}\mathit{\_}\mathit{b}\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{b}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$