2.1790   ODE No. 1790

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

$$-h(y(x))+3(1-y(x))y(x)y^{″}(x)-2(1-2y(x))y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 22.636 (sec), leaf count = 182

$$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}-\frac{1}{(1-K[2]{)}^{2/3}K[2{]}^{2/3}\sqrt{2{\int }_1^{K[2]}-\frac{h(K[1])\exp (-2(\frac{2}{3}\log (1-K[1])+\frac{2}{3}\log (K[1])))}{3(K[1]-1)K[1]}dK[1]+c_1}}dK[2]\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{(1-K[3]{)}^{2/3}K[3{]}^{2/3}\sqrt{2{\int }_1^{K[3]}-\frac{h(K[1])\exp (-2(\frac{2}{3}\log (1-K[1])+\frac{2}{3}\log (K[1])))}{3(K[1]-1)K[1]}dK[1]+c_1}}dK[3]\mathrm{\&}][c_2+x]\}\}$$

✓ Maple : cpu = 0.207 (sec), leaf count = 219

$$\{{\int }^{y\left(x\right)}-3\frac{1}{\sqrt{-6{\mathit{\_}\mathit{b}}^2\sqrt[3]{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{{({\mathit{\_}\mathit{b}}^2-\mathit{\_}\mathit{b})}^{4/3}\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\mathrm{d}\mathit{\_}\mathit{b}+9{\mathit{\_}\mathit{b}}^2\sqrt[3]{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\mathit{\_}\mathit{C}\mathit{1}+6\mathit{\_}\mathit{b}\sqrt[3]{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{{({\mathit{\_}\mathit{b}}^2-\mathit{\_}\mathit{b})}^{4/3}\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\mathrm{d}\mathit{\_}\mathit{b}-9\mathit{\_}\mathit{b}\sqrt[3]{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}3\frac{1}{\sqrt{-6{\mathit{\_}\mathit{b}}^2\sqrt[3]{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{{({\mathit{\_}\mathit{b}}^2-\mathit{\_}\mathit{b})}^{4/3}\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\mathrm{d}\mathit{\_}\mathit{b}+9{\mathit{\_}\mathit{b}}^2\sqrt[3]{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\mathit{\_}\mathit{C}\mathit{1}+6\mathit{\_}\mathit{b}\sqrt[3]{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{{({\mathit{\_}\mathit{b}}^2-\mathit{\_}\mathit{b})}^{4/3}\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\mathrm{d}\mathit{\_}\mathit{b}-9\mathit{\_}\mathit{b}\sqrt[3]{\mathit{\_}\mathit{b}(\mathit{\_}\mathit{b}-1)}\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$