@Rouben Rostamian  last attempt,  how about this problem 

• pde := Omega*(diff(c(y, t), t))-Omega*Lambda*sin(t) = diff(c(y, t), y, y)
• bc := (D[1](c))(0, t) = 0, (D[1](c))(1, t) = 0
• I could not implement the boundary condition
• pde2.mw

@Rouben Rostamian  sorry sir, mistake  

1.Omega*(diff(B₁(y, t), t))+u = diff(B₁(y, t), y, y)   

2.Omega*(diff(B₂(y, t), t))+pe*diff(u(x,y), x) = diff(B₂(y, t), y, y)  

 equation (1) was the problem. I thought the question can be solved directly through maple.   

@Rouben Rostamian sir, the actual pde was

Omega*(diff(c(y, t), t))+pe*diff(c_0*u(x,y), x) = diff(c(y, t), y, y)   

and Given  profile of the velocity u=6*Lambda*(-y^2+y)*cos(2*Pi*x)+1

pde can be expressed in this form c=B₁pe*diff(c₀,x)+B₂c₀            c₀≠c₀(y,t) 

then i have got 2 equations. 

 1. Omega*(diff(c(y, t), t))+u = diff(c(y, t), y, y)   

 2. Omega*(diff(c(y, t), t))+pe*diff(u(x,y), x) = diff(c(y, t), y, y)    

• @Rouben Rostamian Sir, but this is not working pde1.mw. 
• c does not depend on x. In this case, c is the only function of y&t
• Is there some other way to get a solution.
• Omega=100 and Lambda= 0.001 , pe =10