ODE
\[ (k-x+1) y'(x)+n y(x)+x y''(x)=0 \] ODE Classification
[_Laguerre]
Book solution method
TO DO
Mathematica ✓
cpu = 0.041458 (sec), leaf count = 24
\[\left \{\left \{y(x)\to c_1 U(-n,k+1,x)+c_2 L_n^k(x)\right \}\right \}\]
Maple ✓
cpu = 0.095 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}\left (-n,\,k+1,\,x\right )}+{\it \_C2}\,{{\sl U}\left (-n,\,k+1,\,x\right )} \right \} \] Mathematica raw input
DSolve[n*y[x] + (1 + k - x)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*HypergeometricU[-n, 1 + k, x] + C[2]*LaguerreL[n, k, x]}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+(1+k-x)*diff(y(x),x)+n*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*KummerM(-n,k+1,x)+_C2*KummerU(-n,k+1,x)