Solve using the Laplace transform the initial-value problem: x′′ + 4x′ + 5x = 1 and x(0) = x′(0) = 0.

Q: (2s-8.4) find the inverse transform of s2+0.4s–0.21 -

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Q: Show that the Fourier transform of f (x)= e*/2 is e

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Q: -t yい-yle1-224) yloloo, y'lo).3

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Q: Find the Fourier transform of the given function. (a) f(x) = A(2x + 1). A(2x − 1)

A: As per the question we are given the function f(x) as : f(x) = Λ(2x+1) • Λ(2x-1) And we have to find…

Q: Compute the Fourier transform of the following function: f(x) = e-a(r-x0)²+iqx (5) where a > 0 and q…

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Q: Find the Fourier Transforms of the indicated function: f (x) = e-3x for x > 0 and f (x) = e2x for x…

A: We have,fx=e-3xx>0e2xx<0 To Do: Find the Fourier Transform of the given function.

Q: y" + y = -2 sin t + 10 8(t – 7), y(0) = 0, y'(0) = 1.

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Q: B. Find the inverse Z-transform of X(z) Z-1

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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: Determine the Fourier transform and plot the magnitude S1, It| < T/2 l0, otherwise (ii) x(t) = f(x)…

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Q: Find the Fourier transform $\tilde{f}(p)$ of the function 4x²e-5¹ for x ≥ 0 for x < 0. f(x) = {…

A: fx=4x2e-5xfor x≥00for x&lt;0

Q: Find the Fourier transform of (x) (13x if|x] 1

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Q: Use Laplace transform technique to solve y+2y+2y=e, y(0) = 3, y (0)=-3

A: We need to use Laplace transform to solve this differential equation.

Q: e. dt2 d²y dy + 4y = 8t – 10, y(0) = 1, y'(0) = 7 dt f. 3- dy 3– 2 - y = 2y – 1, y(0) = 7,y'(0) = 2…

A: Since you have posted multiple question and according to guidelines we will solve only one question.…

Q: Б) у —у +Зу — 5у%3D—-бе-t У () %3 1, у (0) %3D2, у' (0) %3D— 4

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Q: Solve the initial value problem using the Laplace transform.

A: Given initial value problem is y'''(t)+5y''(t)+9y'(t)+5y(t)=t2ety(0)=0, y'(0)=0, y''(0)=-2…

Q: Solve the fourier transform of the following functions: 2. f(x) = {x if 0 < x < a otherwise

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Q: Find the Fourier transform of (а) f (г) %—D еxp (-ах?), () f (») — еxp (-а \x),

A: To find the Fourier transform of the below functions. fx=e−ax2 fx=e−ax

Q: Use the Laplace transform to solve x₁ = 2x1 + 3x₂ + 12e¹ x2 = x1 +4x2 with initial data x₁ (0) = -8…

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Q: Find the function with the transform 12e-4s î(s) = (2s + 1)²

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Q: Suppose a function f(x) = x between 0 and 1, and f(x) = 0 elsewhere. Solve for the fourier transform…

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Q: 7/2 Q5:-(3t°-2t* – te 3sin 6t +4 cos 4t)eC + t e3t -St As 360 48 (S-2)5 (s-2)5 18 (s-2)²+36 4(S-2)…

A: Answer of question (i) has  typing error

Q: 1. g(t) 3D 4x(t)e/2n4(0) + Зу(t) 2. g(t) = 2y(t) 3. д(t) %3D х(t —2)у(4t) 4. g(t) = 8(t) * y(t) dt

A: Fourier transformation is given by: x(t)=X(f)y(t)=Y(f) 1.)   g(t)=4x(t) ei2π4t+3y(t) Apply Fourier…

Q: Laplace solves the Initial Value Problem Find by transform.

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Q: y" + 2y' + y = te24 , y (0) = 1, y' (0) = 0 -2t

A: To solve the above differential equation we use the partial fraction and table of Laplace transform.…

Q: Find the Fourier transform of f(t) = 5e-3|t|_ %3D

A: To determine the Fourier transform of the below function. ft=5e−3t