ODE
\[ -a y(x)+(c-x) y'(x)+x y''(x)=0 \] ODE Classification
[_Laguerre]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0234825 (sec), leaf count = 24
\[\left \{\left \{y(x)\to c_1 U(a,c,x)+c_2 L_{-a}^{c-1}(x)\right \}\right \}\]
Maple ✓
cpu = 0.097 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}\left (a,\,c,\,x\right )}+{\it \_C2}\,{{\sl U}\left (a,\,c,\,x\right )} \right \} \] Mathematica raw input
DSolve[-(a*y[x]) + (c - x)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*HypergeometricU[a, c, x] + C[2]*LaguerreL[-a, -1 + c, x]}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+(c-x)*diff(y(x),x)-a*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*KummerM(a,c,x)+_C2*KummerU(a,c,x)