8.198   ODE No. 1788

$$\boxed{{\displaystyle 2y\left(x\right)(-1+y\left(x\right))\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-(3y\left(x\right)-1){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+4y\left(x\right)\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)(f\left(x\right)y\left(x\right)+g\left(x\right))+4{\left(y\left(x\right)\right)}^2(-1+y\left(x\right))({\left(g\left(x\right)\right)}^2-{\left(f\left(x\right)\right)}^2-\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)-\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right))=0}}$$

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

Mathematica: cpu = 1.564699 (sec), leaf count = 85 $$\text{DSolve}[-4(1-y(x))y(x{)}^2(-f^{\prime }(x)-f(x{)}^2-g^{\prime }(x)+g(x{)}^2)+4y(x)y^{\prime }(x)(f(x)y(x)+g(x))-2(1-y(x))y(x)y^{″}(x)+(1-3y(x))y^{\prime }(x{)}^2=0,y(x),x]$$

Maple: cpu = 0.219 (sec), leaf count = 113 $$\{\sqrt{y\left(x\right)}-2\frac{\frac{\partial }{\partial x}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{-1/4{\mathrm{e}}^{-2\int f\left(x\right)\mathrm{d}x+2\int g\left(x\right)\mathrm{d}x}{\mathit{\_}\mathit{C}\mathit{1}}^2\mathit{\_}\mathit{Y}\left(x\right)-2g\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})}{\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{-1/4{\mathrm{e}}^{-2\int f\left(x\right)\mathrm{d}x+2\int g\left(x\right)\mathrm{d}x}{\mathit{\_}\mathit{C}\mathit{1}}^2\mathit{\_}\mathit{Y}\left(x\right)-2g\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\}){\mathrm{e}}^{-\int f\left(x\right)\mathrm{d}x+\int g\left(x\right)\mathrm{d}x}\mathit{\_}\mathit{C}\mathit{1}}=0\}$$