Use the Laplace transform to solve the following initial value problem: y" - 1y - 30y = 0 y(0) = −4, y'(0) = 2 First, using Y for the Laplace transform of y(t), i.e., Y = = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, Y(s) Y(s) = Now by inverting the transform, find y(t) = = A s+a + where a < b B 8+6

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'…

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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: Using Laplace Transforms, solve the following differential equation: y" + 10y = 98 where y(0)=0 and…

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Q: Consider the following initial value problem: x" 5x14x = sin(8t), x(0) = 2, x' (0) = -1. Using X for…

A: In your answer this will be 696 place of 632

Q: Using Laplace transform methods, solve for t > 0 the following differential equation, d²r d.r 5 + 6x…

A: The given initial value problem is d2xdt2-5dxdt+6x=2, x0=0, x'0=0. Solve the initial value problem…

Q: Q1-Solve the ordinary differential equation using Laplace transform ý(t) + 2ý(t) + y(t) = sin t…

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Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an…

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Q: Consider the initial value problem +36-cos(64), (0) - 6, (0) 3. a Take the Laplace transform of both…

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Q: Transform the differential equation y" +10y" - 25y' - 250y=9e-t y(0)=0 y' (0) = 0 y" (0) = 1 into an…

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Q: Consider the initial value problem y" – 5y' – 4y = sin(t) y(0) = 5, y'(0) = 2 A. Use the Laplace…

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Q: Equa

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Q: xy" – 2(x + 1)y' + (x + 2)y = 0.

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Q: Consider the following initial value problem: x" - 5x²14x = sin(8t), x(0) = 2, x' (0) = -1. Using X…

A: We will use Laplace transformation table  f't  = s Fs− f0f'' t= s2 Fs − s f0 − f0Lsinat=aa2+s2

Q: Use Laplace transforms to solve the differential equation: y' +y – et = 0 where y (0) = 0, y (0) = 0

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Q: Prove by induction Bernoulli’s Identity: For every real number x > −1 and every positive integer n,…

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Q: When solving a differential equation using the Laplace transform, you apply the Laplace transform to…

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Q: The differential equation is as follows: d[RL] -[RL]k2 dt with initial conditions, [RL], = [RL];=0…

A: So, we will have to use [ RL ]0  as a value in here, and hence, it will be treated as a constant.…

Q: Use the Laplace transform to solve the following initial value problem: y' + 8y = 0 y(0) = 3, y(0) =…

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Q: Find the polynomial f(x) for which a f(x-1)=(x-3) f(x), Vx E R.

A: A polynomial characteristic is a characteristic in an equation that includes handiest non-terrible…

Q: Consider the initial value problem I' + 3r = 45t, r(0) = 2. a. Take the Laplace transform of both…

A: Given differential equation is x' +3x =45 t,   x0=2

Q: Consider the following initial value problem: y" ly 30y = sin(7t) Using Y for the Laplace transform…

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Q: In this problem you will derive the formula for the Laplace transform of the second derivative of a…

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Q: Consider the following initial value problem: x(0) = 2, x' (0) = -1. Using X for the Laplace…

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Q: y" — y' = 2x, y (0) = 1, y'(0) = -2

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Q: 7y" +46y" 175y' - 1150y = 4e t y(0) = 0 y (0) 0 y" (0) = 1 into an algebraic equation by taking the…

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Q: Solve differential equation using Laplace transform ý + 3ý + 2y = 4 with y (0) = 0, ý(0) = 1

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Q: Considel the initial value problem y" – 4y' + 8y = sin(8t) y(0) = 8, y'(0) = 7 A. Use the Laplace…

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Q: Use the Laplace transform to solve the following initial value problem: x' = 9x + 4y, y = -5x + et…

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Q: Consider the following initial value problem: x" – 2x' – 24x = sin(7t), x(0) = 5, x'(0) = -1. Using…

A: Given differential equation is

Q: Use the Laplace transform to solve the following initial value problem: x' = 13x +5y, y = -8x + est…

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Q: Use the Laplace transform to solve the following initial value problem: x' = 12x + 4y, y = −8x + et…

A: We solve given DE by using Laplace Transform.

Q: Use the Laplace transform to solve the following initial value problem: y" + 16y = 0, y(0) = 8,…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…