The inverse forms of the results in Problem 49 in Exercises 7.1 are s-a 2¹ 6²}- | (sa)² + b²) and x{15. { y(t) b (s = a)² + Use the Laplace transform and these inverses to solve the given initial-value problem. y' + y = e-4t cos 3t, y(0) = 0 eat cos bt +b²}. b²) eat sin bt.

Q: For ut + aux = 0 (a) Write down an implicit difference method (backward Euler difference in both x…

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Q: The Fourier transform of the function f(x)=1 ; |x|<2, is 2 sin 2p (c) F(p)=. 2 sin 2p (a) F(p) = sin…

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Q: 1- 3s Find the Inverse Laplace Transform of G (s) =- s2+ 8s +21 13 8 (1) = – 3e -d"cosh(V51) +…

A: Given Gs=1-3ss2+8s+21 to find the inverse Laplace transform Solution:-

Q: Find the Fourier transform off (x) defined by Example 6. 1, |x| a f(x) = sin s ds (ii) 00 sin sa.…

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Q: a) Evaluate £{est}. b) Evaluate L{(t− 3)² + sin 7t + cos 8t} c) Use the Laplace transform to solve…

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

Q: Q1) Solve 1 + cos y – 2xy) dx – (xsin y + x²)dy = 0 +1

A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

Q: Use Laplace transform to solve the following initial-value problem. У" - 2у +5у%3D1+t;y(0)3 0;y'…

A: Given The given problem is y"-2y'+5y=1+t y0=0y'0=4 Use Laplace transform formula…

Q: Use a Fourier transform to solve the following initial value problem for the free Schrödinger…

A: Given: Let us consider the given ut=iuxx ; ux,0=e-x2

Q: 1 Solve the integral equation S f(x – t)e-at dt - f(x) using Fourier transform x² + b² -00 to find…

A: Definition of Fourier Transform : Let f(t) be defined for all t∈(-∞,∞).Then the fourier…

Q: Transform: F (s) 18-16 s²-08-13 Of(t) = 4e 3 sin2t – 4e-3t 31 cos2t O f(t) = 4e³t cos2t 4c sin2t O…

A: Given: F(s)=4s-16s2-6s+13 To find the inverse Laplace transform.

Q: 10.3 Show that the setdown under a standing wave system is a?k 7(x) = (cosh 2kh cos 2kx – 1) 4 sinh…

A: Answer is mentioned below

Q: Activity 1: The motion equation of damped mass-spring system as shown in Fig. 1 below is given as…

A: As per our guideline we can solve only first three subparts.Please repost for another question.…

Q: D) y y(0) c) y" + 4y + 3y = 8(t-2), y(0) = 1, y'(0) = -1

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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: Verify the following equation. F[sin(wot)H(t)] ولا 2 - ل + - [8(w + wo) - 8(w - wo)].

A: The objective is to evaluate convolution of the sine function and Heaviside function with initial…

Q: Use the Laplace transform to solve the given initial-value problem. y' - 3y = 8(t - 4), y(0) = 0…

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Q: Question 7 2s +3 Find the Inverse Laplace Transform of F (s) = s2+4s + 13 A f(t 2sin3t--cos3t 3…

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Q: B: The Laplace transform of the; f(t) = e-t.sinh 3t

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: 3- Suppose that a signal x(t)is given by x(t) = te ³¹ u(t). Compute the Fourier Transform X(w) of…

A: As per the question we are given the following time domain function : fx(t) = te-3t u(t) And we have…

Q: Find solution of equation 2 o(x) = 2f cos(x-1t) ø(1)dir

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Q: (a)x - x = 2t x(0) = 1 x(0)/ = -2

A: As per the policy of bartleby the provisions is to solve only one question at a time

Q: A dynamic system is described with the following differential equation: *+4x+20x = f(t), x(0)=1,…

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Q: evaluate r(g(1)) using the Chain Rule. dt r(1) = (4 sin 2r, 6 cos 21), g(1)=1²

A: Given: rt=4sin2t,6cos2t ,gt=t2

Q: Question3: A. Find the general solution of the following first-order ODE xy' = y + 2x³ sin² (²)

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Q: Question 2 ( a) Evaluate L{eot} b) Evaluate C{(t−2)² + sin 6t + cos 7t} c) Use the Laplace transform…

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Q: a) Evaluate {e-3¹(cosh² t)}.

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: 1. Calculate the complex Fourier coefficients for -7<t <0 0 <t < 7 [Write your answer without sin,…

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Q: Solve the following nonhomogeneous ODES. (a) y" = -4y + e2#; (b) y" – 4y + 3y = e²; (C) y" = y+ e²…

A: Given that  The following differential equation  To find the general solutions

Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: Problem 8.6. 1. Let X ~ xỉ. Show that its moment generating function is given by 1 M1(t) = V1- 1 –…

A: Problem can be solved using concept of moment generating function and gamma function.