a) Find solution u of the PDE uyy + 4u = 0 depend on x and y? %3D b) Find the displacement w(x, t) of an elastic string (c 1) subject to the following conditions: (i) The string is initially at rest on the x-axis from x 0 to ∞ ("semi-infinite string"), (ii) For t> 0 the left end of the string (x = 0) is moved in according to 0.5) and 0.02(1 - t) if (0.5

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A: 2y''+y'+2y=f(t),  y(0)=0, y'(0)=0 Put f(t)=δ(t-5)      at t0=5 ⇒2y''+y'+2y=δ(t-5)

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A: Applying linear approximation we have

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A: Solution:   Given that, Atightly strtched flexible string has its end   fixed at x=0 and x=l. At…

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