The infinite series u (x, t) = > Bn COS 5nt sin nx n=1 is the solution of the wave equation = 2502u 0 < x < T,t > 0, u (0, t) = u (T, t) = 0, t> 0, ut (x, 0) = 0, 0< x

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A: solution:-

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A: Let's find equation of curve in the form of x=h(y).

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A: Solution

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A: We will solve the given wave equation by variable separable method.  Let u(x,t)=X(x)T(t) is the…

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A: As per our guidelines, I can answer maximum one question. Since you have asked for three, So i did…

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A:

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A: Real signal is given by: x(n)↔X(w) Since, X(w)=∑n=-∞∞x(n)e-jwn And, x(n)=abc Take w=0,…

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A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

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A: Inner product of two functions

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A: Since you have asked multiple questions in single request.so we will answering only first question.

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A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

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A:

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A: We will find out the required solution.

Q: (a) Solve the inhomogeneous 1st order equation Uz - Ut = cost U (x, 0) = 0.

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A: In this question, we solve the wave equation by using the method of separation of variables.

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A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

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A: Dear student, there is a mistake in the question. The second derivative should be…