2.1082   ODE No. 1082

\[ y(x) \left (\frac {\left (m^2-v^2\right ) g'(x)^2}{g(x)}+g'(x)^2\right )-y'(x) \left (\frac {(2 m-1) g'(x)}{g(x)}+\frac {g''(x)}{g'(x)}\right )+y''(x)=0 \]

✗ Mathematica : cpu = 0.279223 (sec), leaf count = 0

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]
 

, 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 = 0.243 (sec), leaf count = 74

dsolve(diff(diff(y(x),x),x)-(diff(diff(g(x),x),x)/diff(g(x),x)+(2*m-1)*diff(g(x),x)/g(x))*diff(y(x),x)+((m^2-v^2)*diff(g(x),x)^2/g(x)+diff(g(x),x)^2)*y(x)=0,y(x))
 

\[y \left (x \right ) = {\mathrm e}^{-i g \left (x \right )} g \left (x \right )^{2 m} \left (\operatorname {KummerM}\left (\frac {1}{2} i m^{2}-\frac {1}{2} i v^{2}+m +\frac {1}{2}, 2 m +1, 2 i g \left (x \right )\right ) c_{1} +\operatorname {KummerU}\left (\frac {1}{2} i m^{2}-\frac {1}{2} i v^{2}+m +\frac {1}{2}, 2 m +1, 2 i g \left (x \right )\right ) c_{2} \right )\]