Exercise II Use the method Laplace transform to solve the following. (a) = 1₂-1₁ +1₁ 2²₂2 = 1₂.

Q: у" — Зу' + 2у %3D2е3t y(0) 3D 0 у'(0) — 4 |-

A: Given differential equation is  y''-3y'+2y=2e3t given condition is  y(0)=0 ,y'(0)=4

Q: Solve the Laplace Transform of the equation f(t)= sin3t/t

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Q: Using Laplace transform, solve the following simultaneous equations: y₁+3y1 - y2 u(t-1)et, Yo…

A: We solve given simultaneous equation by using Laplace transform.

Q: y" - 5y' +6y=et; y(0) = 0; y'(0) = 2

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Q: Use the properties to find Fourier transform. f(t) -10 -5 5 10 t (ms)

A: The given curve can be approximated to:

Q: Use the method Laplace transform to solve the following. (a) 2r' + 7r=3e-t, x(0) = 4. (b) 2r' +…

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Q: 14. x" + y = -101 sin(10t) ; y " + x = 101 sin(10t) ; x(0) = 0, x ' (0) = 6, y(0) = 8, y' (0) = -6

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Q: -t yい-yle1-224) yloloo, y'lo).3

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Q: SET UP AND INTEGRATE AND GET TO THE FINAL RESULT FIND THE LAPLACE TRSNSFORM OF THE GIVEN FUNCTION…

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Q: t3 - 3t2 + 5t – 8

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Q: use the Laplace transform to solve the initial value problem.

A: It is required to solve the initial value problem using laplace transform:

Q: t も c6 10. XCt)> { -8 + -8 t ct-6)? » t >6

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Q: y" + y = f(t) y(0) = 1, y'(0) = 0 donde f(t) = { si 0<t< sen(t) si t22 1 ㅠ 2

A: As per the question we are given the following initial value problem :y'' + y = f(t)  ,  y(0) = 1  ,…

Q: x* (t) – x(t) = 4 cost with x(0) = 0, x' (0) = 1 %3D y = 2e with y(0) = – 1 y - y = e -* with y(0) =…

A: Take the Laplace transform on both sides of the equation.

Q: yct)= sin 2t cos 34

A: Given: y(t)=sin2t cos3t

Q: SOLVE FOR THE LAPLACE TRANSFORM. Provide the step-by-step solution

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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: Suppose solving an equation by Laplace transform results in 6 s Y(s) = s² + 64° Evaluate y(").

A: y(s)=ℒ(6ss2+64) =-3(2si(8s)-π)sin(8s)-6cos(8s)ci(8s) y(π)=-3(2si(8π)-π)-6cos(8π)si(8π)

Q: Find Fourier transform for the following functions:x(t)=3+(sin2wt)2

A: Given function is, xt=3+sin2wt2.      ........1 Fourier transformation: Fourier transformation of…

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: 0 = (0)₁ h = (0₂h ! (7) 4₁5 = ht+₁ 46-₁6

A: We have to find the solution of differential equation using laplace transform.

Q: y" + 2y" + y' = eº, y(0) = 0, y'(0) = 1, y"(0) =

A: laplace transform

Q: 3rd ORDER IVP y"" + 2y" — y' - 2y = sin 3t

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Q: y" – y' – 2y = 4t², y(0) =1 y'(0) = 4 I| |

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Q: Use Laplace transform to solve the initial value problem of the ff DE.

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Q: How the Laplace transform method is applied to a higher dimensional PDE, illustrate with example.…

A: We have Laplace transform method is applied to a higher (Two) dimensionalPDE with example.

Q: 15. Find the value(s) of y such that the solution of the initial-value problem y" – 4 y = sin x;…

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Q: Find Laplace transform of the function t2 Sint.

A: Find Laplace transform of the function t2 Sint.

Q: · y"(t)+5y'(t)+4y(t) = 0, y(0) = 1, y'(0) = 0

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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: 5. 2y"+3y"-3y'– 2 y = e',

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Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

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

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Q: y" + 5y' + 4y = 0, y(0) = 1 y'(0) = 0

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