By trial and error, find a solution of the diffusion equation ut = uxx with the initial condition u(x,0) = sin x.
a) u(x,t) = e⁻t * sin x
b) u(x,t) = e^t * sin x
c) u(x,t) = sin(x-t)
d) u(x,t) = e⁻t * cos x