8.201   ODE No. 1791

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

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

Mathematica: cpu = 20.225068 (sec), leaf count = 164 $$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}-\frac{e^{\frac{1}{2}(12-12K[2])}}{(K[2]-1{)}^3\sqrt{2{\int }_1^{K[2]}-\frac{h(K[1])\exp (-2(6(K[1]-1)+3\log (K[1]-1)))}{K[1]-1}dK[1]+c_1}}dK[2]\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{e^{\frac{1}{2}(12-12K[3])}}{(K[3]-1{)}^3\sqrt{2{\int }_1^{K[3]}-\frac{h(K[1])\exp (-2(6(K[1]-1)+3\log (K[1]-1)))}{K[1]-1}dK[1]+c_1}}dK[3]\mathrm{\&}][c_2+x]\}\}$$

Maple: cpu = 0.249 (sec), leaf count = 90 $$\{{\int }^{y\left(x\right)}\frac{1}{{(\mathit{\_}\mathit{b}-1)}^3{\left({\mathrm{e}}^{\mathit{\_}\mathit{b}}\right)}^6}\frac{1}{\sqrt{-2\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{{\left({\mathrm{e}}^{\mathit{\_}\mathit{b}}\right)}^{12}{(\mathit{\_}\mathit{b}-1)}^7}\mathrm{d}\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{{(\mathit{\_}\mathit{b}-1)}^3{\left({\mathrm{e}}^{\mathit{\_}\mathit{b}}\right)}^6}\frac{1}{\sqrt{-2\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{{\left({\mathrm{e}}^{\mathit{\_}\mathit{b}}\right)}^{12}{(\mathit{\_}\mathit{b}-1)}^7}\mathrm{d}\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$