\[ y(x) \left (\frac {\left (m^2-v^2\right ) g'(x)^2}{g(x)}+g'(x)^2\right )-y'(x) \left (\frac {(2 m-1) g'(x)}{g(x)}+\frac {g''(x)}{g'(x)}\right )+y''(x)=0 \] ✗ Mathematica : cpu = 0.614736 (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 = 0.201 (sec), leaf count = 74
\[\left \{y \left (x \right ) = \left (c_{1} \KummerM \left (\frac {1}{2} i m^{2}-\frac {1}{2} i v^{2}+m +\frac {1}{2}, 2 m +1, 2 i g \left (x \right )\right )+c_{2} \KummerU \left (\frac {1}{2} i m^{2}-\frac {1}{2} i v^{2}+m +\frac {1}{2}, 2 m +1, 2 i g \left (x \right )\right )\right ) g \left (x \right )^{2 m} {\mathrm e}^{-i g \left (x \right )}\right \}\]