(a) The function p(x, t) satisfies the partial differential equation a4 dt in 0 x...

 

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(a) The function p(x, t) satisfies the partial differential equation a²4 dt² in 0 ≤ x ≤ 1 for t≥ 0, with 0 < d < u, and satisfies the boundary and initial conditions φ(0, t) = φ(1,t) = 0, dø +2dº_0² dt dx² -(x, 0) = 0. dt +20 ad dx Use separation of variables to find the most general form of p(x, t). (b) If [14 marks p(x,0) = e-2x sin 2лx, find the solution when v = 2. Plot the graph of at x = as a function of t. (a) The function p(x, t) satisfies the partial differential equation a²4 dt² in 0 ≤ x ≤ 1 for t≥ 0, with 0 < d < u, and satisfies the boundary and initial conditions φ(0, t) = φ(1,t) = 0, dø +2dº_0² dt dx² -(x, 0) = 0. dt +20 ad dx Use separation of variables to find the most general form of p(x, t). (b) If [14 marks p(x,0) = e-2x sin 2лx, find the solution when v = 2. Plot the graph of at x = as a function of t.