General pathline of a particle x at point epsilon at time ta

Homework Statement

Show that the path line of a particle at point x currently, and point ξ at time τ is given by

ξ(τ) = x + (τ-t)Lx

Homework Equations

Pathline is solution to
dx/dt = u
x
(t)|t=τ = X

L
is the velocity gradient and is a 2nd order tensor Lij = dui/dxj

The Attempt at a Solution

I am not really sure how to start, any hints or leads on how to begin proving this?
I know how to obtain pathlines if the velocity field is given in terms of x,y,z,t (via integration) but how do I integrate the equations to obtain a general equation with a velocity gradient?

Thanks