2.1084   ODE No. 1084

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

$$-y^{\prime }(x)(\frac{2f^{\prime }(x)}{f(x)}-\frac{g^{\prime }(x)}{g(x)}+\frac{g^{″}(x)}{g^{\prime }(x)})+y(x)(-\frac{f^{″}(x)}{f(x)}+\frac{f^{\prime }(x)(\frac{2f^{\prime }(x)}{f(x)}-\frac{g^{\prime }(x)}{g(x)}+\frac{g^{″}(x)}{g^{\prime }(x)})}{f(x)}-\frac{v^2{g}^{\prime }(x{)}^2}{g(x{)}^2}+g^{\prime }(x{)}^2)+y^{″}(x)=0$$ ✗ Mathematica : cpu = 0.859994 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 0.086 (sec), leaf count = 21

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_v\left(g\left(x\right)\right)f\left(x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathit{Y}}_v\left(g\left(x\right)\right)f\left(x\right)\}$$