Utilize the Laplace transform to find a solution for the given initial value problem: y"-5y'- 36y= 8(t-6) y (0) = 0, y₁ (0)=0 Utilize step(t-c) for Uc(t) y(t)=_

Q: Use the Laplace transform to solve the initial value problem y' +4x²y = -28 -25 (t-1) +S(t-1), y(0)…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: æ' + x = 2+ 8(t – 1), x(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = help…

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Q: Use the Laplace transform to solve the given initial-value problem. y' - 5y = 8(t - 4), y(0) = 0…

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Q: 3. (LT-1) Use the Laplace transform to find the solution to the following initial value problem: y"…

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Q: Use the Laplace transform to solve the given initial-value problem. y' - 2y = 5(t – 4), y(0) = 0…

A: The solution is given as

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: Solve using the Laplace transform y' + 2y = 12 e3t , y(0) = 3

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Q: Use the Laplace transform method to solve initial value problem y + 4y = 2t² + t and y(0) = 3, y'(0)…

A: Given equation is,. y''+4y'=2t2+t and y0=3,y'0=0 Taking Laplace to transform both sides we get,…

Q: f(x) = -12-21x + 18x^2 - 2.75x^3 what method will give a root of the function equal to - 0.287425 in…

A: We will use a numerical method to determine what will be the value of root of the given function in…

Q: The orthogonal trajectories of the family of curves y = cx² is (A) 2x +y2=k (B) x²+2y² = k © x=ky² D…

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Q: 3. 2y" + Зу" — Зу' — 2у %3D е-t, con y(0) 3D 0, у'(0) — 0, у" (0) %3 1

A: Given: 2y'''+3y''-3y'-2y=e-t, y(0)=0=y'(0), y''(0)=1 To find: Solution of given differential…

Q: a' +x = 6+ 8(t – 4), x(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = help…

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Q: 2. Use the Laplace Transform to solve the following system x'= x-5y, y'=-5x+y, x(0)=1, y(0)=1.

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Q: 10) Use the Laplace transform to solve the given initial-value problem. y'-y = 2 cos (3t) when y(0)…

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Q: Solve the equation y" - 2y' +2y=t, y(0) = y'(0) = 0 using the Laplace transform.

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Q: (6) Solve the Integro-differential equation: +4y +5 y(t) dt = e-t; y(0) = 0 dx (7) Find the Fourier…

A: Given Integro-differential equation is dydx+4y+5∫0xy(t) dt = e-t y(0)=0 The given equation can be…

Q: Solve the initial value problem y'' - 2y' + 2y=e2t   y(0) = 0, y'(0) = 0 using Laplace transform.

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Q: Please find the requested derivative of the following functions. s²-4st+t² = 4, find 25 ds dt - ds…

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Q: Please help me solve using the Laplace Transform y''-7y'+10y =9cos(t)+7sin(t)            y(0) = 5,…

A: solution:Given the differential equationy''-7y'+10y=9 cos t+7 sin t   y0=5, y'0=-4Taking laplace…

Q: 22) Solve using Laplace Transform y" + 2y' +5y = etsint where y(0) = 0, y'(0) = 1

A: Solution to the differential equation by using Laplace transform

Q: ý + 16y = 8 (t – ) sin (2t), y(0) = 0, ÿ(0) = 0

A: The solution is given by using some formulas of Laplace transform as follows :

Q: y''-3y'+10y=e-2t , y(0) =0, y'(0)=1

A: We have to solve given problem:

Q: Solve the initial value problem using Laplace Transform of: y'' - 3y'+10y = e-2t when y(0)=0,…

A: Given initial value problem is y''-3y'+10y=e-2t,y0=0, y'0=1 To find the solution of the equation.

Q: 6. Use the Laplace Transform to solve the initial value problem: y' +9y = e-tcos (2t), y(0) = 0

A: Given that the initial value problem y'+9y=e-tcos2t   , y0=0    .

Q: Q6. Solve the partial differential equation by using the Laplace transform: ди du +5=21², with the…

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Q: Use the Laplace transform to solve the initial value problem y" + 3y +2y = sin(2t) where y(0) = 2…

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Q: Use the Laplace transform to solve the given initial-value problem y' + 9y = e-9t, y(0) = 3

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