2.1719   ODE No. 1719

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

$$a{y}^{\prime }(x{)}^2+f(x)y(x)y^{\prime }(x)+g(x)y(x{)}^2+y(x)y^{″}(x)=0$$ ✗ Mathematica : cpu = 41.968 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 0.524 (sec), leaf count = 70

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