2.1096   ODE No. 1096

\[ (a+x) y(x)+x y''(x)+y'(x)=0 \]

✓ Mathematica : cpu = 0.0078782 (sec), leaf count = 61

DSolve[(a + x)*y[x] + Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{-i x} U\left (\frac {1}{2} i (a-i),1,2 i x\right )+c_2 e^{-i x} L_{-\frac {1}{2} i (a-i)}(2 i x)\right \}\right \}\]

✓ Maple : cpu = 0.108 (sec), leaf count = 39

dsolve(x*diff(diff(y(x),x),x)+diff(y(x),x)+(x+a)*y(x)=0,y(x))
 

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