Use the Laplace transform to solve the given initial-value problem. dy dt y(t) = 1 - exp(-t) sinh(t) cos(√2 t) -√2 2 + 3t exp(t) - 1 cosh(t) √3+ sin(√3 t) 2t - 1 0 No solution -y= 1, y(0) = 0 = 1,

Q: Find Laplace transform of x(t)=t (cos)^2 (wt)u(-2t). *

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Q: Find F′(x).

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Q: a - Find h (Stet sinh t sint dt)

A: The objective is to find ∫te-3tsintsinhtdt It is known that, sint=et-e-t2isinht=eit-e-it2…

Q: g(t) = 8t4e5tu(-t)

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Q: sinh ot + cos ot

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Q: . Find the Laplace transform of the function f(t) = 2t + 3 cos(3t) + 4 sin(3t)

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Q: 3. [32] −1 4-3 4. 5. [. |_3 -4 2 1 2 -1 4,

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Q: Find the differential operator which will annihilate the function 2x + r³ – sin 2r.

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Q: Determine L[f]if S() = f(1) = | sin(t - T)e-dt.

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Q: Find an implicit general solution for the ODE dy/dx = [2(2y−x)] / (x+y)

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Q: Use the variation of parameters to find the general solution of the following ODE. z'' + z = tan2 x

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Q: 2x + 2y %3D 1. Use implicit differentiation to find dy/dx for ey

A: GIVEN ex2y =2x+2y

Q: Ejercicio. Evalúe [1?+1 dt dx Ejercicio. Derive F(x) = cos t dt 2

A: The objective is to solve the above questions.

Q: find dy/dx. g(x) = cos x/sin2 x

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Q: Find the differential dy of the function y = 4x²-x+ 3 Select one: O a. (8x-1)dx O b. (x²-x² + 3x) dx…

A: Solve for the differentiation

Q: Both x and ydenote functions of i that are related by the given equation. Use this equation and the…

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Q: Find the Fourier transform of the following function: 7 sin(3r – 2) r2 + 25 - 2 exp (4 - 5|r-3|).

A: We are given a function in variable x and we have to find its Fourier transform. For that we will…

Q: = sin 2 t, 2 n <t < 4 n and f (t) = 0 otherwise, in terms Represent f(t) of unit step function and…

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Q: A(x) = sintdt d. A(x) = ₁ It-2|dt

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