2.1082   ODE No. 1082

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

$$y(x)(\frac{(m^2-v^2)g^{\prime }(x{)}^2}{g(x)}+g^{\prime }(x{)}^2)-y^{\prime }(x)(\frac{(2m-1)g^{\prime }(x)}{g(x)}+\frac{g^{″}(x)}{g^{\prime }(x)})+y^{″}(x)=0$$ ✗ Mathematica : cpu = 0.554805 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 0.371 (sec), leaf count = 74

$$\{y\left(x\right)={\left(g\left(x\right)\right)}^{2m}{\mathrm{e}}^{-ig\left(x\right)}(\mathit{U}(\frac{i}{2}{m}^2-\frac{i}{2}{v}^2+m+\frac{1}{2},2m+1,2ig\left(x\right))\mathit{\_}\mathit{C}\mathit{2}+\mathit{M}(\frac{i}{2}{m}^2-\frac{i}{2}{v}^2+m+\frac{1}{2},2m+1,2ig\left(x\right))\mathit{\_}\mathit{C}\mathit{1})\}$$