please use matlab to solve the problem

2. Let u(x, t) be the solution of the initial/boundary value problem for the heat equation: 22 a u=u a. t a 2 ulx,0) = 0, 400,+) = 2 (1,7) = 2 ) (a) Find u(x, t). lim (b) What is tu(x,t) (c) Use the equilibrium solution and one term from the Fourier series of u(x,t ) to estimate how long from t=0 it will take for u(1/2, ) to attain a half of its equilibrium value (in other words, estimate the value of Tsuch that 1 ulat tull, t) fort ulz,d ) > Lul 1, t) fort? T 2