2.1081   ODE No. 1081

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

$$-\frac{a^{2}y(x)f^{\prime }(x{)}^2}{b^2+f(x{)}^2}+\frac{f(x)f^3(x)y^{\prime }(x)}{b^2+f(x{)}^2}+y^{″}(x)=0$$ ✗ Mathematica : cpu = 0.796893 (sec), leaf count = 0 , could not solve

DSolve[-((a^2*y[x]*Derivative[1][f][x]^2)/(b^2 + f[x]^2)) + (f[x]*(f^3)[x]*Derivative[1][y][x])/(b^2 + f[x]^2) + Derivative[2][y][x] == 0, y[x], x]

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

$$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+\frac{f\left(x\right)\left(\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}f\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)}{{\left(f\left(x\right)\right)}^2+b^2}-\frac{{\left(\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)\right)}^2{a}^2\mathit{\_}\mathit{Y}\left(x\right)}{{\left(f\left(x\right)\right)}^2+b^2}\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$