I am struggling with the following question:
Find all the solutions of the equation
(d/dt (u(x,t))) -(d/dx (u(x,t))) +2u(x,t)=0
Hint: a change on coordinates to simplify (d/dt (u(x,t))) -(d/dx (u(x,t)))
Any help woyld be appreciated.
To the OP. If you introduce a change of variable from to then from the chain rule
so your original problem becomes
If you can chose r and s such that
and , the your PDE becomes - and ODE!
Here's one choice
See how that goes.