I have PDE that I am unable to solve and thought maybe someone could help me. Its a more difficult problem but we'll see if you guys can handle it

its a PDE about flow through a chanel where h is the height of the channel going from 0 to 1

I need the analytic solution the following problem

u(y,t) -> du/dt = -dp/dx + 1/Re_chan * d^2u/dx^2

Re_chan = density*U*h/μ = U*h/v

assume density = 1, U*h = 1

initial condition is u(y,0) = 0

boundary conditions are
u(0,t)=0 y=0 is bottom of the channel
u(1,t)=0 y=1 is top of the channel

use dp/dx = -.001 and Re_chan = 100