3. Use the method of separation of variables to find the periodic solution of the initial value problem U₁ = 2UTI - u(x,0) = 3 + cos T u(x + 2n, t) = u(x, t) -∞0 0; sin r+sin 3x -∞0 < x <∞0; -∞ 0.

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: 1. Find f(x, y) obeying = - sin(x)y and f(0, y) = }(y +2)². %3D %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: (b) The differential equation is given as , x2y''-2xy'+x2+2y=0              .....1