2.1713   ODE No. 1713

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

$$-y(x)(g^{\prime }(x)-y(x{)}^2{f}^{\prime }(x))+y^{\prime }(x)(f(x)y(x{)}^2+g(x))-y^{\prime }(x{)}^2+y(x)y^{″}(x)=0$$ ✗ Mathematica : cpu = 20.7906 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 0.546 (sec), leaf count = 54

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right),[\{\frac{f\left(\mathit{\_}\mathit{a}\right){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2+\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathit{\_}\mathit{C}\mathit{1}+\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-g\left(\mathit{\_}\mathit{a}\right)}{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)}=0\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=y\left(x\right)\},\{x=\mathit{\_}\mathit{a},y\left(x\right)=\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\}])\}$$