Solve the following initial value problem (IVP) of y" – 3y - 10y = 2 where y(0) = 2 and y (0) = -1. First, get the Laplace transform. Then on the choices, determine the solution for y(t) by inverting the transform. O y(t) = - +4e-# - * O yle) = - + 금e+ O vt) = - +4e * +* -2t

Q: 1. f(t) = 5(e^-4t)[cos(10t)] A. (5s – 20) / (s^2 - 8s + 116) B. (s - 4) / (s^2 - 8s + 116) C. 50 /…

A: Laplace transferom of the function

Q: Question* The Laplace transform of f(t) = et-2 cos(2t-4) u(t- 2)-e-(cos(3t) - 1)

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Q: Problem 5 Using Laplace transform, solve y" - 4y + 7y = 0 y(0) = 3, y'(0) = 7

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Q: 4. f(t) = e^(5t)(t^3) A. 6/ (s-5)^4 B. 6/ (s+5)^4 C. 6/ (s-5)^3 D. 6/ (s+5)^3 %3D

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Q: Solve the following Initial Value Problem using Laplace transform: y" – 15y + 14y= e" -10t y(0) = 1,…

A: We are given that;y''-15y'+14y =e-10t; y(0)=y'(0)=1Taking laplace transforms on both the sides;s2…

Q: into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace…

A: Given                   with              Take Laplace transform on both sides then…

Q: 4 None of the Choices f(t) 1 (e²+ e ²¹)-(e₁-e²₁) Option 3

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Q: Find

A: We use definition of Z-Transform.

Q: Find the inverse laplace transform of the followings; a)  X(s)=(s+2)/(s^2+2s+5)…

A: a) Xs=s+2s2+2s+5 Apply Laplace Inverse transform…

Q: What is the Laplace transform, Y(s) for 3y" + 2y'-y 5 where y(0) = y'(0) = 0? %3D a. (3s-1)(#+1) b.…

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Q: 18. 9y" – 6y' + y = 0, y(0) = 3, y'(0) = 1 %3D

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: 10. Solve the following IVP using Fourier Transform: -00 0, u(x, 0) = e¯**, -00 <x < o0. %3D

A: Given: Let us consider the given, ut=uxx,              -∞&lt;x&lt;∞,   t&gt;0ux,0=e-x2,…

Q: 13. x" = -2x + 2y, y" = 2x - 5y; x(0) = 2, x ' (0) = 3, y(0) = 1, y' (0) = 2

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Q: Let L(y(t)} = Y (s) Which of the following can be obtained when Laplace transform applied to the…

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Q: 1. Solve the following difference equation by using Z-transform by replacing the value of M as per…

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Q: Let A be an eigenvalue of a square matrix A and a E R\{0}. Can you find an eigenvalue for aA? Let B…

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Q: The Laplace Transform of d(t) = * O -1/(s+6) O 1/(s-6) 1-/s O 1/s O 1/s^2 O 1 O 1/s^3

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Q: 2) find the fourier transform x(t) = u(t) x(t) ulzt) x²(t) = u(+ + 5) -

A: xt=utxt=u2txt=ut+5xt=ute-jw0t

Q: y"+2"-z' = 0 y' + z 221-ex - Yo = 0, y = 1 20= 1, 2 = 1

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Q: 2. Let 2s6 s³3s2 + 4s - 12 Find the inverse Laplace transform, y(s). Y(s):

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Q: What is the inverse Laplace transform of 1 /[(s-2) ^2 + 9]? C. 3e^ (-2t) D. 2 sin (2t) 5. A. sin…

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Q: 7. Graph the function f(t)=2U(t-1)-3U(t-2) and find its Laplace Transform 8. Write the function…

A: Remark : As per new guildline,  in case  of posting multiple question we will answer of only first…

Q: 1. Deduce the continuous function whose Laplace Transform is 10 F(p) P (p² + 9) 2.Find Р2—ЗР+10 (i)…

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Q: Which of the following is the expression to be ob tained when the Laplace transform is applied to…

A: We are given the differential equation :  2y''-3y'-2y=te2t Applying Laplace transform to both the…

Q: 5. 2y"+3y"-3y'– 2 y = e',

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Q: Find the Fourier transform of the following functions: (₁) f(t)= (11) "-(1+t), -12 t ≤0 t-1 04+ ²1 อ…

A: We have to find the Fourier transform of the given functions: (i) ft=-1+t-1&lt;t≤0t-10&lt;t≤10t&gt;1…

Q: the Inverse Fourier Transform x(t) of each signal X(w) given below. X(w) = -4 sinc² X(w) = πd(w − 1)…

A: "Since you have posted multiple questions, we will provide the solution only to the specified sub…

Q: Find the transform of the function below. g(t) = (t^2)*sin(2t) A) (16s^2-12) / (s^2+4)^3 B…

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Q: Given that the Fourier transform of e- πt^2 is e- πs what is the Fourier transform of the following…

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Q: 3. Which of the following is the Laplace transform of sin (2t) - 2tcos (2t) ? A. s^2 / (s^2 + 4) ^2…

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Q: Determine the Fourier transform of the following signal: _(t+1) u(t+1) x (t) = è

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Q: 4 10 (2-A) 1 2 Jet O 5. Use Laplace transform to solve y' + y = e²x.

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Q: Suppose the Fourier transform F(w)=re-lwl, is known. Show that the inverse Fourier transform, viz.,…

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