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 = 0.171613 (sec), leaf count = 36
\[\left \{\left \{y(x)\to e^{-x} (c_1 U(a-b,a,x)+c_2 L_{b-a}^{a-1}(x))\right \}\right \}\]
Maple ✓
cpu = 0.343 (sec), leaf count = 33
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-x} \KummerM \left (a -b , a , x\right )+\textit {\_C2} \,{\mathrm e}^{-x} \KummerU \left (a -b , a , x\right )]\] 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))
Maple raw output
[y(x) = _C1*exp(-x)*KummerM(a-b,a,x)+_C2*exp(-x)*KummerU(a-b,a,x)]