3. Use a Fourier transform to solve the equation d²y dx2 y 0 with initial conditions y(0) = yo and y 0 as x oo,

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

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Q: (3) Solve the initial value problem using Laplace transform. y + 4y sin 3t, y(0) = 5.

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Q: By using method of Laplace Transform, solve the initial value problem of d²y dx2 dy 3 + 2y = e¬t dx…

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Q: Use the Laplace transform to solve the given initial-value problem. y' - y = 2 cos(9t), y(0) = 0…

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Q: How do you solve this problem?

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Q: 3. Use the Laplace transform method to solve the initial value problem r = 6x1 + 11r2, r = -4x1 –…

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Q: dy = et. dt Find the solution when y(0)=2 using the method of Laplace transform

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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: use the laplace transform to solve the initial value problem y"+2y'+2y=cos(2t) with y(0)=0 and…

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Q: By using method of Laplace Transform, solve the initial value problem of d²y 3- dx2 + 2y = et dx…

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

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Q: Solve by Laplace transform method x' = 2x – 2y у'3 х — у — cos t x(0) =,y(0) = 3 4

A: Solution: The system is x'=2x-2y y'=x-y-cost x0=35,  y0=45

Q: use laplace transform to solve the initial value problem y′′ + 16y = 4cos(3t) + δ(t-π/3) , where…

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Q: Use laplace transform to solve the initial value problem; a) y''+9y=cos3t,y(0)=2, y'(0)=5.

A: We shall use Laplace and inverse Laplace transform to solve this

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

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

A: To solve the following problem on lapace transform of differential equations

Q: 2. [. | Solve the initial value problem using Laplace transform y" -4y'+ 4y 3te", y(0)=4, y'(0)=2

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

A: Given below the detailed solution

Q: 04 Obtain the particular solution for: 2y" +2y= 2 sinx y(0)=0, y'(0)=1 (a) By using Laplace…

A: The solution is given below in the next step:

Q: Use the Laplace transform to solve the initial value problem y" – 2y' – 8y sin 3t, y(0) = 0, y'(0) =…

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Q: 10. Use the method of Laplace transform to solve the initial value problem y" – 2ay + (a? + B²)y =…

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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: у" + 6у' + 10у %3D 1, У (0) %3D —1, y'(0) = 2

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Q: Use the Laplace transform to solve the given initial-value problem. y" +y = 2 sin(2t), y(0) = 11,…

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Q: Determine the Laplace transform of the differential equation 3y’’’ – y’ = e-3t t5 - 9y’’ + 4y With…

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

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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: Use the Laplace Transform to solve the initial value problem. y’’ – 3y’ + 2y = e^(-4x) ; y(0) = 1 ,…

A: The given differential equation is: y''-3y'+2y=e-4x Take Laplace transform both sides and linearity…

Q: Use the Laplace transform to solve the given initial-value problem y" + y = 2 sin(2t), y(0) = 11,…

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Q: 6. Use Laplace transform to solve the initial value problem: y" - 2y' + 2y = et, y(0) = 0, y'(0) =…

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Q: Use the Laplace Transform to solve the initial value problem. y" -6y + 13y 0, y(0) = 0, y ((

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Q: Solve the initial value problem using a Laplace Transform. y "+ 2y' - 3y = sin (2x) ;      y (0) =…

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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: 25. а. Apply Fourier transform to solve: ди for 0 < x, t 20 Under the conditions,

A: Given,              ∂u∂t=∂2u∂x2,  for  0≤x, t≥0           (1)Under the conditions,…

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y""+ 2y" - y' - 2y =…

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Q: Solve the initial value problem using Laplace Transform Method y'' - 4y = sin 2t  ; y(0) = 3,…

A: To solve: The initial value problem using Laplace Transform Method y'' - 4y = sin 2t  ; y(0) = 3,…

Q: Use Laplace Transform technique to solve the initial value problem y' + 2y = 26 sin 3t , if y(0) = 3

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Q: Use the Laplace transform to solve the given initial-value problem. y""+ 2y" -y - 2y = sin(4t), y(0)…

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Q: 7) Solve the initial value problem using the Laplace Transform L. y" – 8y' + 20y = te', y(0) = 0,…

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Q: Solve the nonhomogeneous differential equations y" + 25y = 18 cos(4x) + 18 sin(4.x). Do not use the…

A: Solution of given differential equation is the sum of complementary and particular solution

Q: Use Laplace transforms to solve the initial value problem x"+4x' +13x= te^-t; x(0)=0,x '(0)=2

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Q: 2. Use the Laplace transform to solve the initial value problem y" + 4y' +8y = sint, y(0) = 1,…

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Q: Solve the given differential equation using Laplace Transform (D2 – 6D + 15)y = 2 sin 3t - With the…

A: GIVEN (D2-6D+15)y=2 sin 3twith intian condition y(0)=-1, y(0)'=-4we need to solve the equation using…

Q: Solve the initial value problem using Laplace Transform: d²y dy + 5- dx + 6y = 0, y(0) = 0, y(0) = 1…

A: The solution is given as

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = = y"" + 2y" - y' - 2y =…

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Q: 3) Use the Laplace Transform to solve the Initial Value Problem. y(0) = 1, y'(0) = 0 y" – 2y'+ 5y =…

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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: 4. Use Laplace transform technique to solve, y"+2y'+y=4e given y(0) = 2 and y'(0) = -1

A: We have to find general solution of given differential equation using Laplace transform Method.

Q: Solve the initial value problem by using the Laplace transform. y"-5y +6y=4 sin 3r, y(0)=0 and y'(0)…

A: We know L{ y"(t) } = s^2 y(s) - sy'(0) -y(0)  L{ y'(t) } = s y(s) - y(0)