Exercise 3-3: Given the wave equation utt = uxx, with the following conditions Boundary Condition: u(0,t) = te-t Initial Conditions: u(x, 0) = 0, ut (x, 0) = 0 on the domain x > 0 and t> 0. (a) Sketch the function u(0,t) = tet on the interval 0 < t < 5. Label the time, t*, when the function is maximum. Your sketch can be by hand, or on a computer (include your code) (b) Imagine we are describing the motion of a string. Describe the initial conditions and bound- ary conditions, in words. (c) Solve the PDE. Hint: Recall that the wave equation utt = cur has a general solution u(x,t) = F(x- ct) + G(x + ct) where F(x - ct) represents a disturbance that propagates to the right at speed c and G(x + ct) propagates to the left.