Solve the initial-value problem y"(t) – 4y'(t) + 4y(t) = 4e2t; y(0) = –1, y' (0) = –4.

Q: (6) y" +16y = g(t), y(0)=0, y (0)=1, %3D g(t) = { 1, 0<t< T 0, %3D

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Q: y" + y = √2 sen √2t, y(0) = 10, y'(0) = 0

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Q: (cos(t - 27/3 ) t> 2/3 .Find I f(t) if f(t) = t<0

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Q: 2 Calculate the inverse Laplace of by using Convolution theorem s(s2 +2s+4)

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Q: Find the Laplace Transform of the function. Show your work. f(x) = sinh(ax)

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Q: Use the Laplace transform to solve the initial-value problem x" + 4x = f(t), x(0) = 0, x'(0) = 0,…

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Q: 10. Find the Laplace transform of 10 cos Tt (1 < t < 2)

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Q: Use the Laplace transform to solve the given initial value problem. For technical reasons, write u…

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Q: a) 2-3u(t-5) cost = -t Find the 33 Ordine Lap of

A: The given function is ht=-t cos5t-3ut-5cost To find: the Laplace transform of the given function.

Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: _-_-7/57 = 1778 ++ (5)) pust

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Q: 3s – 137 L(f) s2 + 2s + 401

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Q: 1 F(@) = %3D 2 - w2+j3w

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Q: 3. Solve y" – 2y' + 5y = 0, y(0) = 5, y'(0) = -3.

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Q: 10. Solve F (1) =1 +2 F (t- u) e 2" du.

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Q: Find the solution of the Initial Value Problem given below by using the Laplace transform method.…

A: Given initial value problem, y'''-5y''+17y'-13y=cos2t,y0=0, y'0=0, y''0=1 To find the solution of…

Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: Find the Laplace transform of f(t)=u(t− 3)(2t² +1)+2e³ cos²t

A: The objective is to find the laplace transform of f(t).

Q: 2s Prove that L(t sin t) (s²+1)²

A: We can use the concept of Laplace transform in order to solve the given problem.

Q: Problem 1: Solve the following Initial Value Problem: y" – 4y' + 5y = 4e", y(0) = 2, y' (0) = 7 %3D…

A: Answer is mentioned below

Q: L[e-3tcos (3t) + 3e-3tsin (3t)]

A: The solution is given as

Q: Use the Laplace transform to solve 1 x = 4x + 1y y' = x(t) = y(t) = - 29x - 6y x(0) = 2, y(0) = - 12

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Q: Find the transform. Show the details of your work. Assume that a, b, w, 0 are constants. 1 k 1 a)…

A: we have to find the Laplace transformation for the given  (a) Now the equation for the line joining…

Q: x"(t) + 4x" (t) + 9x'(t) + 10x(t) = -24te'; when t = 0, x = 0, x' = -4, x" = 10

A: Use Laplace table

Q: a) Given that f(t) = {(tt) ((t-1)² e3t 0 ≤t≤1 t>1 i) Find Laplace of f(t) using the definition of…

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Q: Laplace Transform

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