2.1790   ODE No. 1790

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

$$-h(y(x))-2(1-2y(x))y^{\prime }(x{)}^2+3(1-y(x))y(x)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.585538 (sec), leaf count = 186

$$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}-\frac{1}{(1-K[2]{)}^{2/3}K[2{]}^{2/3}\sqrt{c_1+2{\int }_1^{K[2]}-\frac{\exp (-2(\frac{2}{3}\log (1-K[1])+\frac{2}{3}\log (K[1])))h(K[1])}{3(K[1]-1)K[1]}dK[1]}}dK[2]\mathrm{\&}][x+c_2]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{(1-K[3]{)}^{2/3}K[3{]}^{2/3}\sqrt{c_1+2{\int }_1^{K[3]}-\frac{\exp (-2(\frac{2}{3}\log (1-K[1])+\frac{2}{3}\log (K[1])))h(K[1])}{3(K[1]-1)K[1]}dK[1]}}dK[3]\mathrm{\&}][x+c_2]\}\}$$ ✓ Maple : cpu = 1.339 (sec), leaf count = 119

$$\{{\int }^{y\left(x\right)}-\frac{\sqrt{9}}{3}\frac{1}{\sqrt{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)(\mathit{\_}\mathit{C}\mathit{1}-\frac{2}{3}\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}{({\mathit{\_}\mathit{b}}^2-\mathit{\_}\mathit{b})}^{-\frac{4}{3}}\mathrm{d}\mathit{\_}\mathit{b})\sqrt[3]{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}\frac{\sqrt{9}}{3}\frac{1}{\sqrt{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)(\mathit{\_}\mathit{C}\mathit{1}-\frac{2}{3}\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}{({\mathit{\_}\mathit{b}}^2-\mathit{\_}\mathit{b})}^{-\frac{4}{3}}\mathrm{d}\mathit{\_}\mathit{b})\sqrt[3]{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$