Mathematica
eq = (vi - xi) D[f[xi], xi] == f[xi];
DSolve[eq, f[xi], xi]
(* {{f[xi] -> C[1]/(vi - xi)}} *)
Matlab
syms vi xi f(xi)
dsolve( (vi -xi)*diff(f)==f)
ans =
C2/(vi - xi)
Maple
restart;
dsolve((vi - xi)*diff(f(xi),xi)=f(xi),f(xi));
(* f(xi) = _C1/(vi-xi) *)