y' -y = t et sint, y(0) = 0

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

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Q: y" - 3y' =f(t), y(0) = 1, y'(0) - 1 %3D 8 Given L{f(t)}= S-2 2 S+1

A: Given initial value problem is y''−3y'=ft, y0=1,y'0=−1 And given Lft=8s−2−2s+1 We know that…

Q: Solve the initial value problem using Laplace transform y" – 4y'+4y= 3te", y(0)=4, y'(0) = 2

A: The given question is related with Laplace transform. Given that,                    y'' - 4y' + 4y…

Q: y" + y = f(t), y(0) = 0, y'(0) = 1. Here 0, 0 37. f(t) =

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Q: Solve the initial value problem using Laplace transforms?

A: Given:- dy/dt + 3/125y = 0.48, for 0 < t < 10- dy/dt + 3/125y = 0.72, for t ≥ 10 Step 1: Solve…

Q: 1 -s F(s) = e = -+ s2 e-3s

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Q: x" + 16 x = cos 4t, x(0) = 0 ve x(0) = 1

A: We have to first take Laplace transform of the given differential equation.

Q: The general solution of the initial value problem given below is the "Laplace Transform". find using

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: -t yい-yle1-224) yloloo, y'lo).3

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Q: y" + 2y' + 5y = 10e¬2", y(0) = 0, y'(0) = 0.

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Q: y" + 3y/ + 2y = e-t, y(0) = 0, y'(0) = 2.

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

A: laplace transform

Q: Find Lf" sin /6t-r'e"}

A: Please see below

Q: y" (t) + 8y'(t) + 25y(t) 0; y(0) = 1, y(0) = 2

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Q: y" + 4y = 8t, y(0) = 2, y'(0) = 0.

A: Here we will use Laplace transform to solve the Initial value problem.

Q: y" + 4y' + 8y = sent y(0) = 1 y'(0) = 0 %3D %3D

A: Answer will be in Laplace inverse form, this can not simplify.

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: Find the general solution for the following differential equation: y" – y" + y' – y = t² + cost -

A: I have find complementary function and particular integral separately and we get the required…

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

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Q: d?y = v2sin/2t; with y(0) = 10, y(1)(0) = 0 %3D dt2

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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: y" + 4y = 26(t – T), y(0) = 1, 3'(0) = 0

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Q: Solve the initial value problem using Laplace Transform

A: As per the question we are given the following second order homogeneous linear differential equation…

Q: y" - 4y' + 4y = cos(t); y(0) = 1, y'(0) = -1

A: Given:The initial value problem is given by,                To Find:We have to solve the given…

Q: Use Laplace Transform to solve the given initial-value problems.

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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: 1. y"- 2y' + 5y = 0; y(0)%3D2, %3D y'(0) = 4.

A: We know that L{y''}=s^2Y(s) -sy(0) -y'(0)  And L{y'}=sY(s) -y(0)

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

A: