ODE
\[ (a+x) y'(x)+b y(x)+x y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0293648 (sec), leaf count = 36
\[\left \{\left \{y(x)\to e^{-x} \left (c_1 U(a-b,a,x)+c_2 L_{b-a}^{a-1}(x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.079 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-x}} \left ( {{\sl U}\left (a-b,\,a,\,x\right )}{\it \_C2}+{{\sl M}\left (a-b,\,a,\,x\right )}{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[b*y[x] + (a + x)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1]*HypergeometricU[a - b, a, x] + C[2]*LaguerreL[-a + b, -1 + a, x])/E^x}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+(a+x)*diff(y(x),x)+b*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(-x)*(KummerU(a-b,a,x)*_C2+KummerM(a-b,a,x)*_C1)