I'm in an elementary PDE's class and I'm trying to do problems in my textbook. I'm having trouble starting. I was wondering if someone could show me how to do this example, so I can model similar solutions after it.
Find the solution and give a physical interpretation of the problem uxx = 4ut (i.e. second partial derivative of u with respect to x = 4 times the first partial derivative of u with respect to t)
for 0 < x < 2, t > 0,
with the conditions
u(0,t) = 0
u(2,t) = 0
u(x,0) = 2sin(pi*x/2) - sin(pi*x) + 4sin(2pi*x)