2.1138   ODE No. 1138

\[ y(x) (2 m+4 n-x)+4 m y'(x)+4 x y''(x)=0 \]

✓ Mathematica : cpu = 0.0147862 (sec), leaf count = 38

DSolve[(2*m + 4*n - x)*y[x] + 4*m*Derivative[1][y][x] + 4*x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{-x/2} U(-n,m,x)+c_2 e^{-x/2} L_n^{m-1}(x)\right \}\right \}\]

✓ Maple : cpu = 0.124 (sec), leaf count = 26

dsolve(4*x*diff(diff(y(x),x),x)+4*m*diff(y(x),x)-(x-2*m-4*n)*y(x)=0,y(x))
 

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