ODE
\[ (k-x+1) y'(x)+n y(x)+x y''(x)=0 \] ODE Classification
[_Laguerre]
Book solution method
TO DO
Mathematica ✓
cpu = 0.169617 (sec), leaf count = 24
\[\{\{y(x)\to c_1 U(-n,k+1,x)+c_2 L_n^k(x)\}\}\]
Maple ✓
cpu = 0.334 (sec), leaf count = 25
\[[y \left (x \right ) = \textit {\_C1} \KummerM \left (-n , k +1, x\right )+\textit {\_C2} \KummerU \left (-n , k +1, x\right )]\] 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))
Maple raw output
[y(x) = _C1*KummerM(-n,k+1,x)+_C2*KummerU(-n,k+1,x)]