i) Show that the exact solution of the following heat equation with given boundary and inital conditions U₁ = 2xx 0≤x≤n, 0≤t≤ 0.2 u(x, 0) = sin(2x), 0 ≤x≤n, 0≤t≤0.2 u(0,t) = u(x, t) = 0, is the following function: u(x,t) =e8tsin(2x) ii) Solve the heat equation given in part i) by explicit finite difference method for 1st time level, using h =, k = 0.01. Explicit Finite difference formula for the heat equation ut = cuxx Uj+1 = ru{+1, + (1-2r)u+ru-1 where r ck h²