Sorry, I didnt think the other equations would make a difference to the one in question, which is probably the reason why I've been sweating over this all day.
I'm pretty sure that the constant does equal zero since the initial data gives at t=0, u(x,y=0)
Thanks again for your help
Ok, so I am clearly missing something blindingly obvious:
Initial data: t=0, u(x,y=0) = 2, x < 0 and 1, x > 0
I have 3 characteristic equations given by:
1. du/dt=0 therefore u is constant wrt t
2. dy/dt=1 therefore y=t + constant
Using that at t=0, y=0 we get that constant = 0 and so...
Am I being really stupid?!?
All I know is that u=u(x), and so I don't know how to integrate 1/u wrt x. Surely its not ln(u) because u doesn't equal x?!?
Ive been stuck on this all day and its starting to drive me mad so I am sorry if the answers staring me in the face
Thanks for the quick reply :)
The actual question is to use the method of characteristics to solve a PDE
From this I have obtained that one of the characteristic equations is dx/dt = u, which I need to rearange to get an equation for x in terms of t.
I have also been given the intial data ...
In my differential equations class I have been given a problem which involves solving dx/dt=u where u=u(x)
I know that this is done by separation such that ∫dx/u = ∫dt, and then the constant of integration found using initial conditions, however I am getting myself all worked up and confused as...