You may earn up to 10 points to the total score by solving the following three problems

Solve the problem, plot the graph of the solution using Maple

1. Find the steady-state distribution of the temperature T(x,y) inside the rectangular domain 0 < x < 1, 0 < y < 4, if the boundary conditions are u(x,0)= x, u(x, 4)= x^2, u(0, y)= 0, u(1, y)=1
2. Find the steady-state distribution of the electrical current j(r, t ) in an infinite conducting plane outside the circular hole ( r > 1). The hole is isolated: j.n =0 on the boundary of the hole. The current at infinity is uniform and is directed along the OX axis.
3. Find the distribution of the temperature  T(x,y, t) inside the rectangular domain 0 < x < 1, 0 < y < 1, if the boundary conditions are u(x, 0, t)= x, u(x, 1, t)= 0, u(0, y, t)= 0, u(1, y, t)=1-y and the initial conditions are: u(x, y, 0)=0. The constant of conductivity is equal o one. Plot the graph of u(x, y, 0.05),  u(x, y, 0.5),  u(x, y, 5),