ODE No. 1786

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

$$f(x)(1-y(x))y(x)y^{\prime }(x)+2(1-y(x))y(x)y^{″}(x)-(1-2y(x))y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 0.990839 (sec), leaf count = 95

$$\left\{\{y(x)\to \frac{1}{4}\exp (-i{\int }_1^x{c}_1(-e^{-{\int }_1^{K[3]}\frac{1}{2}f(K[1])dK[1]})dK[3]-i{c}_2)(1+\exp (i{\int }_1^x{c}_1(-e^{-{\int }_1^{K[3]}\frac{1}{2}f(K[1])dK[1]})dK[3]+i{c}_2)){}^2\}\right\}$$ ✓ Maple : cpu = 0.24 (sec), leaf count = 42

$$\{y\left(x\right)=\frac{1}{8\mathit{\_}\mathit{C}\mathit{2}}{(2{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}\int {\mathrm{e}}^{-1/2\int f\left(x\right)\mathrm{d}x}\mathrm{d}x}\mathit{\_}\mathit{C}\mathit{2}+1)}^2{\left({\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}\int {\mathrm{e}}^{-\frac{\int f\left(x\right)\mathrm{d}x}{2}}\mathrm{d}x}\right)}^{-1}\}$$