2.1032   ODE No. 1032

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

$$y(x)(\frac{(\frac{1}{4}-v^2)g^{\prime }(x{)}^2}{g(x)}-\frac{3g^{″}(x{)}^2}{4g^{\prime }(x{)}^2}+g^{\prime }(x{)}^2+\frac{g^3(x)}{2g^{\prime }(x)})+y^{″}(x)=0$$ ✗ Mathematica : cpu = 0.407629 (sec), leaf count = 0 , could not solve

DSolve[y[x]*((g^3)[x]/(2*Derivative[1][g][x]) + Derivative[1][g][x]^2 + ((1/4 - v^2)*Derivative[1][g][x]^2)/g[x] - (3*Derivative[2][g][x]^2)/(4*Derivative[1][g][x]^2)) + Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.252 (sec), leaf count = 48

$$\{y\left(x\right)=(\mathit{\_}\mathit{C}\mathit{2}{\mathit{W}}_{\frac{i}{2}{v}^2-\frac{i}{8},\frac{1}{2}}\left(2ig\left(x\right)\right)+\mathit{\_}\mathit{C}\mathit{1}{\mathit{M}}_{\frac{i}{2}{v}^2-\frac{i}{8},\frac{1}{2}}\left(2ig\left(x\right)\right))\frac{1}{\sqrt{\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)}}\}$$