Solve the following initial value problem using Laplace transform: d²y dt² where 10+21y = g(t), y(0) = -1/3,t=0= 5, Y(-1/3) y (-1/3) = ( ) g (t) J4 0 < t <3 ={4 7 3≤t Let Y (s) be the Laplace transform of the solution y (t). Then evaluate Y (-1/3) y(-1/3).

Q: Suppose solving an equation by Laplace transform results in Y(s) = s2 + 64' Evaluate y(7).

A: We have to solve given problem:

Q: Compute the Laplace transform. Your answer should be a function of the variable s: s(πt)} = c{₁+ +…

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Q: Solve the Laplace Transform of the equation f(t)= sin3t/t

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Q: When calculing the Laplace transform of the function f(t)=e^2t.sin(4t) is obtained as a result:

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Q: 02 Define a Map L: M232M.3 by 1 3. LHA)-1 A, Is L a L2 lincar transformotion? Pove yovy AssertionB

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Q: Find the inverse Laplace transform of the function as + b H(s) = (s – a)2 + 32 °

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Q: Compute the Laplace transform. Your answer should be a function of the variables: L2+ u₂(t)e-³¹…

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Q: Use matrix to solve for X(s) and Y(s) in the equations below and find the laplace transform of X(s)…

A: To solve the given problem Simplify for X(s) and Y(s)  Using inverse laplace transformation solve…

Q: 1 1 s? +4 s -4 (s+3)

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Q: Let f(t) = e^t if 0=1   Write f(t) using step function and find the laplace transform. Also,…

A: We have to write f(t) using step function and find the laplace transform. Also, draw the graph.

Q: Use Laplace transform technique to solve y +2y +2y= e-, y(0) = - 4, y'(0) = - 2

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Q: Use convolution and Laplace transform to evaluate y''+y=sin(t) , y(0)=1 , y'(0)=-1

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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: Solve for the laplace transform x(t) = (t+3) sin(t-6)

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Q: 6) Use a Laplace Transform to solve. y(4) - 4y(3) + 6y" -4y' + y = 0; y(0) = 0, y'(0) = 1, y"(0) =…

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Q: Find the Laplace transform F(s) = L {ƒ(t)} of the function f(t) = (9 – t) (u₂(t) — u6(t))

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Q: The Laplace transform of x(t) is X(s). Given x(0)=2 and x'(0)=-1, write an expression for the…

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Q: Use Laplace transform to solve the following IVP y′′(t) = 4y(t) −e^(−t)U(t −1), y(0) = y′(0) = 0.

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Q: Find the inverse Laplace transform of 7s + 3 82 + 17 8 >0

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Q: Find Fourier transform for the following functions:x(t)=3+(sin2wt)2

A: Given function is, xt=3+sin2wt2.      ........1 Fourier transformation: Fourier transformation of…

Q: How is the existence of the Laplace transform of a function guaranteed?

A: We known that the  Existence of the Laplace transform of a function guaranteed

Q: Find the inverse Laplace transform L-{F(s)} of the function F(s) s2 + 9s – 10 NOTE: The answer…

A: The given problem is to find the inverse Laplace transform of the given function.

Q: Determine the Laplace transform of the equation f (x) = 2e-"sin4t 16 A s2+ 4s + 20 20 B s2+ 4s + 20…

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Q: a"(t) + 16x(t) = 5 sin t, a'(0) = x(0) = 0 %3D

A: First we have to take Laplace transform of the given equation.

Q: Q4. Apply Linearity property of Laplace Transform to find the Laplace Transform of x(t) = 5e-tu(-t)…

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Q: Show how to do the Laplace transform of f(t) = t*cos(w*t) using the table of operational transforms.

A: Given  f(t) =t cos ω t

Q: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t) = -e3it f(t) may be…

A: Here, gt=-e3jtft

Q: What is the Fourier transform of: f(t)=sgn(t) e? Your answer should be expressed as a function of w…

A: Given a function ft=7i2sgnte−8t Explanation ft=7i2e−8t       for t&gt;0 ; t&gt;0 sgnt=1−7i2e8t…

Q: Use formulas from this course to find the inverse Laplace transform (a) L-1{+1) 2s+1 1 252+8 (b)…

A: Solution:

Q: 5 The inverse Laplace transform of F(s) = 5² - 2s+5 1 f(t) = 5e²¹ sin 2t f(t) = 5e¹ sin 2t 5 f(t) =…

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Q: Find the convolution of f(t) = 3t and g(t) = sin (21). You can either calculate f * g directly, or…

A: In the given problem we have to find the convolution of two function f(t) and g(t) using the…

Q: Find the Laplace transform of sinh3 4t

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