Originally Posted by

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

$\displaystyle u_t + cos(\pi x) u_x = 0$ using the method of characteristics. This amounts to solving the following odes:

$\displaystyle dt/ds = 1, t(0) = 0$ which implies $\displaystyle t = s$ and

$\displaystyle dx/ds = cos(\pi x), x(0) = x_0$.

This ode yields (if I'm right):

$\displaystyle |sec(\pi x) + tan(\pi x)| = Ce^{\pi s}$.

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