Question

Prove the Rodrigues formula following the steps below: Let v = x^(n)exp(−x). First show
that xdv/dx = (n − x)v. Then derive that
xd^(n+2)v/dx^(n+2)+ (1 + x)d^(n+1)v/dx(n+1)+ (n + 1)d^(n)v/dx^n= 0 . (4)
Next show that y(x) =exp(x)/n! d^(n)v/dx^(n) is a solution of Laguerre’s differential equation xy"(x)+(1-x)y'(x)+ny=0
using (4)