2.1788   ODE No. 1788

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

$$-4(1-y(x))y(x{)}^2(-f^{\prime }(x)-f(x{)}^2-g^{\prime }(x)+g(x{)}^2)+4y(x)y^{\prime }(x)(f(x)y(x)+g(x))-2(1-y(x))y(x)y^{″}(x)+(1-3y(x))y^{\prime }(x{)}^2=0$$ ✗ Mathematica : cpu = 1.57092 (sec), leaf count = 0 , could not solve

DSolve[-4*(1 - y[x])*y[x]^2*(-f[x]^2 + g[x]^2 - Derivative[1][f][x] - Derivative[1][g][x]) + 4*y[x]*(g[x] + f[x]*y[x])*Derivative[1][y][x] + (1 - 3*y[x])*Derivative[1][y][x]^2 - 2*(1 - y[x])*y[x]*Derivative[2][y][x] == 0, y[x], x]

✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol

$$\{\sqrt{y\left(x\right)}-2\frac{\frac{\partial }{\partial x}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{-1/4{\mathrm{e}}^{2\int g\left(x\right)\mathrm{d}x-2\int f\left(x\right)\mathrm{d}x}{\mathit{\_}\mathit{C}\mathit{1}}^2\mathit{\_}\mathit{Y}\left(x\right)-2g\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})}{\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{-1/4{\mathrm{e}}^{2\int g\left(x\right)\mathrm{d}x-2\int f\left(x\right)\mathrm{d}x}{\mathit{\_}\mathit{C}\mathit{1}}^2\mathit{\_}\mathit{Y}\left(x\right)-2g\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\}){\mathrm{e}}^{\int g\left(x\right)\mathrm{d}x-\int f\left(x\right)\mathrm{d}x}\mathit{\_}\mathit{C}\mathit{1}}=0\}$$