3. Solve the free-end wave equation Utt = 16urz u(r,0) = f(x) = 2 sin(32) u(x,0) = g(x) = 5 -∞ < x < x, t> 0 -∞ < x <∞ %3! %3D ∞ < x < ∞

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

Q: Utt = 16urg u(0, t) = u(7, t) = 0 u(x, 0) = f(x) = sin(x) – 4 sin(3) u(x, 0) = g(x) = sin(2a) 0 0 t…

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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Q: Integrate (a) S2(* dt (b) S(x+1)³ dx (c) cos(-x)(x²)dx

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Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

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Q: y" + 4y' + 3y = sin (e*) %3D

A: follow next step

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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: ANSWER (a): OPTION D is correct f(x) = sin (2x)

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A: We will solve the problem

Q: V ss Vst Vts Vtt || || 11 11 V sin(2s² - 4t²)

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

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A: This is an homogeneous linear differential system. We will solve by this using eigenvalues and…

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A: According to Bartleby's guidelines we can solve only 1 question at a time. Here's the solution for…

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A: We are authorized to solve only 1 question, please repost remaining questions Differential equation

Q: Are these equation separable 1.s2+ds/dt = (s+1)/st 2.dr= b(cosx dr+ rsinxdx) 3.y'=ye(x+y)/(x2+2)

A: The objective of the problem is to determine whether the given equations are separable. A…

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Q: dF Find dx or F(x) COS x 1-) F(x) = S* /1 + t³ dt sin x

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Q: -(v/y)- o None of the above () ferentia uation y"+y' = 1? What is the general solution of the dif-…

A: given differential equation :-             y''' + y' = 1

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A: