Problem 2 (2 points) For u(x,t) defined on the domain of 0x and t0, solve the PDE, It au = ( 127 ) 0 + (187) u ' + G + with the boundary conditions, (i) ux(0,t) = 0, (ii) ux(,t) = 0, (iii) u(x, 0) = 1 + cos(2x) For this problem, we expect a closed-form exact solution with only a finite number of terms and without any unevaluated integral. Expect a deduction if the requirement is not satisfied. Problem 3 (2 points) For u(x,t) defined on the domain of 0 x2023 and t0, solve the PDE, et It = u with the boundary conditions, (i) u(0,t) = 0, (ii) u(2023,t) = 0, (iii) u(x, 0) = sin(x) + sin(2x). For this problem, we expect a closed-form exact solution with only a finite number of terms and without any unevaluated integrals. Expect a deduction if the requirement is not satisfied.