2.1787   ODE No. 1787

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

$$h(y(x))+2(1-y(x))y(x)y^{″}(x)-((1-3y(x))y^{\prime }(x{)}^2)=0$$ ✓ Mathematica : cpu = 1.00351 (sec), leaf count = 170

$$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}-\frac{1}{(K[2]-1)\sqrt{K[2]}\sqrt{c_1+2{\int }_1^{K[2]}\frac{e^{-2(\log (1-K[1])+\frac{1}{2}\log (K[1]))}h(K[1])}{2(K[1]-1)K[1]}dK[1]}}dK[2]\mathrm{\&}][x+c_2]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{(K[3]-1)\sqrt{K[3]}\sqrt{c_1+2{\int }_1^{K[3]}\frac{e^{-2(\log (1-K[1])+\frac{1}{2}\log (K[1]))}h(K[1])}{2(K[1]-1)K[1]}dK[1]}}dK[3]\mathrm{\&}][x+c_2]\}\}$$ ✓ Maple : cpu = 0.34 (sec), leaf count = 80

$$\{-c_2-x+{\int }_{}^{y\left(x\right)}\frac{1}{\sqrt{(c_1+\int \frac{h\left(\mathit{\text{\_b}}\right)}{{(\mathit{\text{\_b}}-1)}^3{\mathit{\text{\_b}}}^2}d\mathit{\text{\_b}})\mathit{\text{\_b}}}(\mathit{\text{\_b}}-1)}d\mathit{\text{\_b}}=0,-c_2-x+{\int }_{}^{y\left(x\right)}-\frac{1}{\sqrt{(c_1+\int \frac{h\left(\mathit{\text{\_b}}\right)}{{(\mathit{\text{\_b}}-1)}^3{\mathit{\text{\_b}}}^2}d\mathit{\text{\_b}})\mathit{\text{\_b}}}(\mathit{\text{\_b}}-1)}d\mathit{\text{\_b}}=0\}$$