Use the Laplace transform to solve the following initial value problem: x' = 13x +5y, y = -8x + est x(0)= 0, y(0) = 0 Let X(s) L{x(t)}, and Y(s) - L{y(t)}. = Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s): X(s) = Y(s) = Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the system of DES: x(t) = y(t)

Q: Solve the differential equation using Laplace Transform. (b) y" – y" + 4y' – 4y = 10e-t, y(0) = 5,…

A: We will find out the required solution.

Q: I want X(s)=

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Q: Let A(x) be the function defined by A(x) = 4 We have A(0) = -3 A'(-1/2) = -2 for x = [-1,0], A(x) =…

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Q: Use the Laplace transform to solve the given differential equation subject to the indicated initial…

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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: Use the method of Laplace transforms to find a general solution to the differential equation below…

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Q: (B Using the Laplace transform, resolve the following differential equation: y' - y = r(t) with…

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Q: Let Solve the differential equation using Laplace transforms. y(t) = t/16+5cos(4t)+95/64sin(4t) g(t)…

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Q: xy" – 2(x + 1)y' + (x + 2)y = 0.

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Q: Show that the transformation z = log tan (x/2) reduces the differential equation d²y +cotr +4x…

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Q: Employ Laplace transforms to solve the differential equation of y"-2y'+y=3e¹* Given y(0)= and y(0) =…

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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: Use Laplace Transformation to solve the differential equation y-2Ky +Ky=2e*(K+cosKx) (0) =1 and…

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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: Given the differential equation y'' + 3y' – 3y = sin(3t), y(0) = -2, y'(0) = 2 - Apply the Laplace…

A: Given that, the differential equation need to solve it using the Laplace transformation.

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

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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: x' + 3x = 9t, x(0) = 4. Take the Laplace transform of both sides of the given differential equation…

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Q: Transform the differential equation Therefore Y = into an algebraic equation by taking 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' = 12x + 4y, y = −8x + et…

A: We solve given DE by using Laplace Transform.

Q: Find the Laplace transform of the following differential equation and express it as a single…

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Q: 5. Find the coordinates of the points on the cross sectional curve of the intersection of the cone z…

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