For u(x,t) defined on the domain of 0<=x<=100 and t>=0, solve the PDE
a) u(x,t) = e(-t)sin(x)
b) u(x,t) = e(-t)cos(x)
c) u(x,t) = e(t)sin(x)
d) u(x,t) = e(t)cos(x)