Trouble with PDE of a channel flow

I am having trouble finding the analytic solution to this problem, any help is appreciated. the @ symbol represents a partial derivative

its an engineering problem of a PDE for starting poiseuille flow in a channel u(y,t)

@u/@t = −dp/dx +1/Rehchan @^2u/@x^2

Rehchan is the reynolds number for the height of the channel

Rehchan = density*U*h/u = U*h(chan)/v

initial condition u(y,0) = 0

boundary conditions

u(0,t)=0 for t>0 y = 0 represents the bottom of the channel
u(1,t)=0 for t>0 y = 1 represents the top of the channel

dp/dx = -.01 and Rechan = 100