A flexible string of length t is tightly stretched between x = 0,x = r, on x-axis, its ends being fixed at these points. When set into small transverse vibration, the displacement y(x, t) from x-axis...

Answer the question in detail and correctly.

Extracted text: A flexible string of length t is tightly stretched between x = 0,x = r, on x-axis, its ends being fixed at these points. When set into small transverse vibration, the displacement y(x, t) from x-axis of any point x at time t is given by - a²y = 4 a²y Find the solution of equation which satisfies y(0, t) = 0, y(n,t) = 0, O) = 0 and y(x, 0) = 0.1 sin x + 0.001 sin 4x for 0 < n.="" t="">