Partial Differential Equation with initial condition on a curve

Question

I recently had an assignment question asking to solve a PDE.
The question is as follows:

Solve $u_t + 3t u_x = u$ with the initial condition $u(x,t)=1+\cos x$ on the curve $x + 3t = 0$.

I know how to solve without the initial conditions, but I would like to know how to solve for the full solution with the initial conditions. Thanks!