1.(a) Find characteristics for the PDE describing u(t, x) for t ? R and x ? R
Hence find the general solution.
(b) Find the solution that satisfies the initial conditions
2. Consider the following equation for u(x,y)
Ã¯Â¿Â½ (a) Assuming x 6=0classify this equation and show that its characteristic equations are given by
(b) Use these characteristics to show that the equation reduces to the standard form:
Ã¯Â¿Â½ Ã¯Â¿Â½(c) Hence find the general solution for u(x,y).
3. solution to the Telegraph equation,
can be obtained by letting E(x,t) = v(t)U (x,t)with a view to removing the first order time derivative.Use this process to obtain the Klein-Gordon equation,