Let L[y(x) = Y(s)the following equation has been obtained when Laplace transformation, has been applied to an initial value problem y(x). Find y(0). Y(s): 25(8 – s?) s(s? + 25)

Q: L[y(x)] = Y(s) the following equation has been obtained when Laplace transformation has been applied…

A: Find the partial fraction and use linearity of laplace inverse

Q: Use Laplace transform technique to solve the initial value problem y" – 4y = e*, y(0) = 0, y'(0) =…

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Q: Consider the initial value problem y" + ay' + by = u(t), y(0) = c, y'(0) = d, t > 0 s² + 2s + 1…

A: Given: To explain the given statement as follows, y(0)=c, y'(0)=d, t>0 To find the constants a,…

Q: [Let Ly(x)] = Y(s) the following equation has been obtained when Laplace transformation has been…

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Q: Use Laplace Transform to solve the initial value problem y' - 2y +2y=cos t y(0) = 0; y'(0)=1 %3D

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Q: Find the Laplace transform of the given differential equation with initial conditions dy - 3y e": y…

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Q: Solve the following initial value problem with Laplace transformation: 2y" – 12y' + 30y = 4 cos(5t),…

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

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Q: If we use the Laplace transformation, the solution y(t) of the following differential cquation: y' -…

A: Given y'-2y =1 and y(0) =2 Applying laplace on both sides       L(y')-L(2y) =L(1) We know that…

Q: use the Laplace transform to solve the initial-value problem 3. y" + y = 6(t -T)+ 6 (t - y(0) = 0,…

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Q: Using Laplace transformation, the solution of the following differential equation y" – y = e2t, with…

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Q: Solve the initial value problem y'' - 2y' + y = 0, y(0) = 1, y'(0) = 0 using Laplace transform.

A: The given equation is: y''-2y'+y=0,y(0)=1,y'(0)=0...(1)

Q: Question * If we use the Laplace transformation, the solution y(t) of the following differential…

A: The given differential equation is  y'-3y=1            ...(1) with y(0)=2. Taking the Laplace…

Q: Use Laplace transformation to solve the initial value problem y' + 2y = u(t) sin (2t), y(0) = w,…

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Q: Transform the initial value problem y" + 5y' + 4y = 0, y(0) = 3, y'(0) = -3 into an algebraic…

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Q: If y(t) satisfies the initial value problem  ((d2y)/(dt2)) -(5(dy/dt))-6y=126H(t-2), y(0)=3,…

A: Given differential equation is d2ydt2-5dydt-6y=126Ht-2 Taking Laplace transform on both sides,…

Q: Use laplace transform to solve the initial value problem; a) y''+2y'=gamma(t-1),y(0)=0,y'(0)=0

A: We have to find Laplace transform of  y''+2y'=gamma(t-1),y(0)=0,y'(0)=0

Q: y" – 2y' + y = 0 y(0) = 1, y'(0) = 0 Solve the initial value problem using Laplace transform.

A: y"-2y'+y=0 Applying Laplace Transform and using the fact that it is linear we get Ly"-2Ly'+Ly=0…

Q: The Laplace transform L{e^-t^2} exists (because it is exponential order), but without finding it…

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Q: Solve the initial value problem by Laplace transform. y" - y' – 2y = e" y(0) = 0 , y'(0) = 1

A: Using Method of Laplace transform.

Q: Using Laplace transformation, the solution of the following differential equation y" +y = 3, with…

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Q: (B) Use Laplace transformation to solve the differential equation √√2e-¹ y+16ym. +6+8y' csc 2x+…

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

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Q: If we use the Laplace transformation, the solution y(t) of the following differential equation: y' –…

A: The given differential equation is                                       y'-3y=1  with  y(0)=2.

Q: 2) Using Laplace Transforms, solve the following initial value problem y" - 4y' - 5y = cosh(2t),…

A: Solution

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Q: If x(t), y(t) solve the initial value problem x'(t) = -2x + 2y + e-", x(0) = 0 у/(0) %3D 2 — Зу.…

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Q: Use the Laplace transform to solve the initial value problem y' -3 y=cos(6 t), y(0) = 6

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

A: laplace transform

Q: y''+4y=u(t)(t-2) , y(0)=y'(0)=0 find the initial value problem with laplace transformation.

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Q: Use the Laplace transform to solve the initial value problem y" + y' – 2y = e# with y(0) =1 and…

A: Given differential equation :

Q: Using Laplace transforms, solve the initial value problem y" − 2y' + 10y = 0, y(0) = -3, y'(0) = 3.…

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Q: Question * If we use the Laplace transformation, the solution y(t) of the following differential…

A: Laplace transformation

Q: If we use the Laplace transformation, the solution y(t) of the following differential eq y' - 3y =…

A: See the detailed solution below.

Q: Example 4: Solve the following differential equation using Laplace transformation: d²y +y = t2 * e',…

A: Given 3dydt-3d2ydt2+y=t2×et

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

A: The answer is given by using properties of Laplace transform.

Q: Transforms

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Q: Solve the following initial value problem using Laplace transformation y" + 2y' + y = te-t, y(0) =…

A: Given differential equation is: y''+2y'+y=te-t Boundary conditions are: y0=1 and y'0=-2 To apply…

Q: (2) Solve the following initial valued problems using the method of Laplace transformation (i) y" –…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Use Laplace transform to solve the initial value problem y" – 2y' +y = e", y(0) = 0, y (0) = 0. %3D

A: Given problem :

Q: [Let L[y(x)] = Y(s) the following equation has been obtained when Laplace transformation has been…

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Q: Transform the given initial value problem into an algebraic equation for Y L{y} in the s-domain.…

A: Let's find.

Q: let L[y(x)] = Y(s) the following equation has been obtained when Laplace transformation has been…

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Q: Use Laplace transforms to solve the initial-value problem: y" (t) – y'(1) + 1 = 0, subject to y(0) =…

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Q: If we use the Laplace transformation, the solution y(t) of the following differential equation: y -…

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Q: [Let Ly(x)] = Y(s) the following equation has been obtained when Laplace transformation has been…

A: Given the Laplace transform of a function y(x)                 Lyx=Ys=491-s2ss2+49 Find y(0).

Q: Evaluate solution of initial value problem y"- 4y' + 3y = 6t – 8, y(0) = 0,y'(0) = 0 by using…

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

Q: If we use the Laplace transformation, the solution y(t) of the following differential equation: y' -…

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Q: Use Laplace transform technique to solve the initial value problem y" – 4y = e*, y(0) = 0, y(0) = 0.

A: Given equation is y''−4y=e3t.....1 and y0=0, y'0=0. We know that Ly''=sYs−sy0−y'0 and Ly=Ys Take a…

Q: dy dy (e) + 4 + 20y = –3 sin 2r, y(0) = y'(0) = 0. dt dr²

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