Partial Differential Equation -- method of characteristics (ode solve)

I've been asked to solve

using the method of characteristics. This amounts to solving the following odes:

which implies and

.

This ode yields (if I'm right):

.

However, I cannot solve this explicitly for x, and therefore cannot solve the pde by the method of characteristics? Can anyone shed insight? Have I done something wrong? Is there a missing trig identity somewhere?

Thanks

Re: Partial Differential Equation -- method of characteristics (ode solve)

Quote:

Originally Posted by

**davismj** I've been asked to solve

using the method of characteristics. This amounts to solving the following odes:

which implies

and

.

This ode yields (if I'm right):

.

However, I cannot solve this explicitly for x, and therefore cannot solve the pde by the method of characteristics? Can anyone shed insight? Have I done something wrong? Is there a missing trig identity somewhere?

Thanks

Your PDE...

... is 'nonhomogeneous' and equivalent to then system...

(2)

...the solution of which is...

(3)

... so that the solution of (1) is...

(4)

... where is any continous function with continous derivative...

Kind regards