ODE
\[ -a y(x)+(c-x) y'(x)+x y''(x)=0 \] ODE Classification
[_Laguerre]
Book solution method
TO DO
Mathematica ✓
cpu = 0.176004 (sec), leaf count = 24
\[\{\{y(x)\to c_1 U(a,c,x)+c_2 L_{-a}^{c-1}(x)\}\}\]
Maple ✓
cpu = 0.331 (sec), leaf count = 17
\[[y \left (x \right ) = \textit {\_C1} \KummerM \left (a , c , x\right )+\textit {\_C2} \KummerU \left (a , c , x\right )]\] 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))
Maple raw output
[y(x) = _C1*KummerM(a,c,x)+_C2*KummerU(a,c,x)]