4.28.28 $ny(x)+x{y}^{″}(x)+(1-x)y^{\prime }(x)=0$

ODE
$$ny(x)+x{y}^{″}(x)+(1-x)y^{\prime }(x)=0$$ ODE Classification

[_Laguerre]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0869933 (sec), leaf count = 21

$$\left\{\{y(x)\to c_{1}U(-n,1,x)+c_2{L}_n(x)\}\right\}$$

Maple ✓
cpu = 0.093 (sec), leaf count = 21

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathit{M}(-n,1,x)+\mathit{\_}\mathit{C}\mathit{2}\mathit{U}(-n,1,x)\}$$ Mathematica raw input

DSolve[n*y[x] + (1 - x)*y'[x] + x*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]*HypergeometricU[-n, 1, x] + C[2]*LaguerreL[n, x]}}

Maple raw input

dsolve(x*diff(diff(y(x),x),x)+(1-x)*diff(y(x),x)+n*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*KummerM(-n,1,x)+_C2*KummerU(-n,1,x)