du 3- at х > 0, t>0 u(0, €) — о , t>о u(x,0) = e¬" x > 0.

Q: 2. f(t) = e4"(t² + 3t + 5)u(t) %3D

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Q: .) Use method of Laplace Transforms. y"-6y +13y=0, y(0) = 1, y (0) = -3.

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Q: Suppose you take out a loan for 160 days in the amount of $14,000 at 7% ordinary interest. After 40…

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Q: 64. Use the finite Fourier cosine transform to solve the heat conduction problem t> 0, 0 0, where…

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Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y" - y'= et cos(t),…

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Q: the Laplace Transforms of the following (t) = 3. You must answer this part by integration, not using…

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Q: By using the Fourier transform, find a solution for the following problem

A: Given: The fourier transform is,  P  ut  t , x  = 4 uxx t , x + t + et  ,   x∈ ℝ , t>0u 0 , x   =…

Q: 3.60. Using the unilateral Laplace transform, solve the following integral equations: (a) y(t)=1+af…

A: Introduction: The Laplace transformation is also used in solving integral equation. Apart from…

Q: Use the method of Laplace transform to solve the initia. value problem: y" - y - 12y = et, y(0) = 2,…

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Q: e inverse Fourier tra |w| e 2 3 N

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Q: y "(t) – y(t) = 4 cos(t); y(0) = 0, y'(0) = 1 Answer: y(t) = 2 cosh(t) + sinh(t) – 2 cos(t)

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Q: 1. Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2,…

A: From first shifting theorem                                                       (…

Q: 5. Laplace Transforms (a) Use the theorem of derivatives of Laplace transforms to: i. 2ks (s²-k²)2.…

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Q: Q3 [CLO 3] Solve the IVP by using Laplace Transform y" -2y'+37y=e +cos 3t, y(0) =0,y'(0) =1.

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Q: 1. Find the Laplace transforms for the given f(t). (h) f(t) = 3 sinh At (i) f(t) = e-2t cos 3t (j)…

A: Solution is given below:-

Q: a. f(t)= et, cost, 0 2TT.

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Q: Consider the heat equation 第= u (0.1)= 0.1 2 0, (r.0) -45 00, 0.0 Applying th Fourier sine transform…

A: Given heat equation is ∂u∂t=4∂2u∂x2, 0<x<∞, t>0u(0, t)=0, t≥0u(x, 0)=f(x), 0≤x<∞ As we…

Q: Use Laplace transform to solve the given IVP. 3. у" — у' %—D еХ cos x, у(0) %3D 0, у'(0) — 0

A: We have y''-y'=excosx  , y0=0 , y'0=0 Now,  Ly'=sYs-y0Ly''=s2Ys-sy0-y'0 Take Laplace transform on…

Q: dx +4x = 2e 3 , x(0)= 5 dt (d) dx +4x = sin 2t , x(0)= 0 dt (e)

A: Laplace transferom, solve the differential equation by using Laplace transferom

Q: 0<t<3 için f(()=e'+0.5 ve T = 3

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Q: 1. A spring with a mass of 2 kg requires a force of 6N to stretch the spring 0.5m beyond its natural…

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Q: Calculate the Fourier transform of the two-sided exponential pulse function given by: l<0 S(1) = 31…

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Q: Find the Laplace transforms for the given f(t). (k) f(t) = t sinh 3t (1) f(t) = t² sin 3t (m) f(t) =…

A: The given function is k ft=t sinh 3tl ft=t2 sin3tm ft=t2 sin2tn fθ=2e3θ4 cos2θ-5 sin2θ We have to…

Q: Use the Laplace transform to find the solution for the following IVP: y″ + y = u5(t) with y(0) = 0…

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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: 4. Use Laplace transforms to solve the following initial value problems. d?x dx (a) +2 +4x = 0 ,…

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Q: Use the Laplace transform to find the solution. for r > 0,t > 0, dy y(0, t) (x,0)% 3 0 for x > 0,…

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Q: Assume that a plane starts to move on a runway according to the Dif. Equ. below. Find the distance…

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Q: ed the ans

A: Given, fx=c-x2cfor x&lt;c0for x&gt;c As it is known that, Fourier transform of fx is given as,…

Q: y" + 5y + 6y = 8(t) + u(t - π) cost, y(0) = 0, y'(0) = 0 11

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Q: Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(0) = 0 Find the general solution. (A y(t) =…

A: Given differential equation is y'' + a2y = 0; y(0) = 1, y'(0) = 0

Q: ind the F(s) Laplace transforms of the following f (t): 1. f(t) = (2e' + 5)u(t)

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Q: olve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" +…

A: In this question, the concept of Laplace Transform is applied. Laplace Transform The Laplace…

Q: t) Consider the following initial value problem: S 7t, 7t, 0 6 Using Y for the Laplace transform of…

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