2.1443   ODE No. 1443

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

$$y^{″}(x)=-\frac{f^{\prime }(x)y^{\prime }(x)}{2f(x)}-\frac{g(x)y(x)}{f(x)}$$ ✗ Mathematica : cpu = 0.271215 (sec), leaf count = 0 , could not solve

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

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

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