Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" – 5x' = 8(t - 4), a(0) = 6, a'(0)= 0. In the following parts, use h(t - c) for the Heaviside function h (t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution a(t). c(t)

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: Use the Laplace transform to solve the given initial-value problem. y' + 5y = e", y(0) = 2 y(t) =

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Q: a) By using the Laplace transform, solve the following differential y" +y = 1- H(1 - 37), y(0) = 0,…

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: Use the Laplace transform to solve the given initial-value problem y' + 4y = e-4t, y(0) = 3 y(t) =

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: Q3 By using method of Laplace Transform, solve the initial value problem of d²y 3. dx2 + 2y = e=t dx…

A: Please check the question. The question should be, d²y/dt² -3dy/dt+2y=e^(-t) subject to y(0)=y'(0)=0

Q: Consider the following initial value problem, in which an input of large amplitude and short…

A: Given, x''-6x'=δ(t-4), x(0)=7, x'(0)=0.   a). We know that,…

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Q: Use the Laplace transform to find the solution of y"+8 y'+Ay=e¯'sint for y'(0)=y(0)=1 & A=25. Then,…

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

A: Given differential equation is,x1+x=4+δ(t-1) ,  x(0)=0      -(1)We know that,L{x'(t)} =L{x(t)}-…

Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: Use the Laplace transform to solve the given initial-value problem. y" + y = 2 sin(2t), y(0) = 11,…

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Q: Use the Laplace transform to find the solution of y"+Ay'+25 y=e'sin t for y'(0)=y(0)=1 & A=6. Then,…

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Q: 1 Find the Inverse Laplace Transform of s2+2s+ 10 (A -e "cos3t 3 1 B -e -'sin9t 3 3r -e"cost D -e…

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Q: Explain your solution to the following problem: use the Laplace transform to solve the given…

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Q: In this exercise we will use the Laplace transform to solve the following initial value problem: y"…

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Q: Given this periodic function: f(t) =1 from 0<t<a and f(t) = 0 from a <t< 2a Solve for the Laplace…

A: Please find attachment for the details solution

Q: Use the Laplace transform to solve the given initial-value problem. y" + 9y = e', y(0) = 0, y'(0) =…

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Q: Use the Laplace transform to solve the given initial-value problem. y"+y= /2 sin(/2t), y(0) = 9,…

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: 2. Solve for the Laplace transform of f(t) = 5 using the long method

A: A detailed solution is given below

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider the following initial value problem: y" – 5y – 6y = sin(9t) y(0) = 1, y'(0) = -2 Using Y…

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