2.1108   ODE No. 1108

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

✓ Mathematica : cpu = 0.0172795 (sec), leaf count = 37

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

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

✓ Maple : cpu = 0.125 (sec), leaf count = 26

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

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