Transport Equation IVP Solution

[Robconway]

Homework Statement

Hi guys, I'm having trouble with a homework problem:

I will have to solve for the IVP of a transport equation on R:

the equations are:

Ut-4Ux=t^2 for t>0, XER
u=cosx for t=0, XER

Homework Equations

transport equation

The Attempt at a Solution

This non-linear transport solution is throwing me off. I don't know if I am supposed to use D'alemberts(As I have been doing for my previous HW problems)
Also, I can't directly solve for the homogeneous equation which in turn makes the u=cos x part very hard to solve

 

[haruspex]

Duplicate of https://www.physicsforums.com/showthread.php?t=701729 ?