8.196   ODE No. 1786

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

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

Mathematica: cpu = 1.028631 (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 = 0.094 (sec), leaf count = 59 $$\{y\left(x\right)=\frac{1}{8\mathit{\_}\mathit{C}\mathit{2}}(4{\left({\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}\int {\mathrm{e}}^{-1/2\int f\left(x\right)\mathrm{d}x}\mathrm{d}x}\right)}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+4{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}\int {\mathrm{e}}^{-1/2\int f\left(x\right)\mathrm{d}x}\mathrm{d}x}\mathit{\_}\mathit{C}\mathit{2}+1){\left({\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}\int {\mathrm{e}}^{-\frac{\int f\left(x\right)\mathrm{d}x}{2}}\mathrm{d}x}\right)}^{-1}\}$$