Given that x(0)=0, apply the laplace transform to find a general solution of tx''-(4t+1)x'+(4t+2)x=0

Q: I need to use the Laplace Transform to solve the given initial value problem

A: We will solve the given differential equation using Laplace transform method.

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: Solve the following dynamics equation using the Laplace transform with the initial conditions x(0) =…

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Q: By using Laplace transform to solve the IVP: y" - 4y' +9y=t, with y(0) = 0 and y'(0) = 1 Then Y(s)…

A: Given IVP is  y"-4y'+9y=t ......(1) y(0)=0,y'(0)=1 .....(2) We fin Y(s).

Q: Use the Laplace Transform to solve the initial value problem y" + 5y + 6y = 6

A: Given, y''+5y'+6y=6 with initial conditions, y0=0, y'0=0. Apply Laplace transform on both sides of…

Q: у" (() + у(t) 3 0 y(0) = 0 y'(0) = 1

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Q: Use the Laplace Transform to solve the given initial-value problem.   2y' + y = 0;  y(0)= -3

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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: The general solution of the initial value problem given below is the "Laplace Transform". find using

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

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 the Laplace transform to solve the given initial-value problem. y" - 5y' = 8et - 4e-t, y(0) = 1,…

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

A: To apply Laplace transform technique to obtain the solution of the given initial value problem

Q: Use differentiation in time domain to solve the the Laplace transform: y"-y'-6y=0; y(0)=6, y'(0)=13

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Q: Use the Laplace transform to solve the given initial-value problem y' + 4y = e-4t, y(0) = 3 y(t) =

A: Given that, Initial value problem is, y' + 4y = e-4t    and     y(0) = 3 We have to solve this…

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: use the Laplace transform to solve the given initial-value problem. dy di -Y= 1 P. | У(0)-0

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Q: 2 – 2e ª +tU(t – 2) + dt те

A: using laplace formula for finding above laplace values....

Q: Use the Laplace transform to solve the initial value problem. x' + 2y' - y = 1; 2x' +y = 0; x(0) =…

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Q: Solve the following initial value problems by Laplace transform technique

A: We have given a differential equation ,  y'' + 2y' + 5y = 50t - 100   ,  y2 = -4  , y'2 = 14 This is…

Q: - 3y' + 2y = e3* when y(0) = y'(0) = 0

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Q: Evaluate equation y’ – 3y' – 4y = e³x using the Laplace transform, with initial conditions y(0) = -5…

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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: Use the Laplace transform to solve the given initial-value problem. 2y+3y" - 3y - 2y = et, y(0) = 0,…

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Q: Q4 Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0)=1 (a) By using Laplace transform…

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Q: Use the Laplace transform to solve the initial value problem y" + 4y = e2t, y (0) = 1, y' (0) = -1.

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

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Q: Use the Laplace transform to solve the given initial-value problem. y" - 3y' = 4e2t - 2et, y(0) = 1,…

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

Q: Solve the following initial value problem using Laplace transform method: y' +6y=e4t; y (0) = 2.

A: We solve by using Laplace Transform.

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"" + 2y" – y' - 2y = sin(3t),…

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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: 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(t) = y""+ 2y" - y' - 2y =…

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Q: Б) у —у +Зу — 5у%3D—-бе-t У () %3 1, у (0) %3D2, у' (0) %3D— 4

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Q: The formula for the Laplace transform of t^ , n! is true for sn+1

A: Option (d) is correct

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 = 5(t-8), y(0) 0.…

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Q: Use the Laplace transform to solve the given initial-value problem. y"+y= √2 sin(√2t), y(0) 13,…

A: Solution:-

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

A: To use: Laplace transform to solve the given initial-value problem. y'''+2y''-y'-2y=sin4t, y0=0,…

Q: Use the Laplace transform to solve the given problem: 3-5y = 0 dx

A: From table of Laplace table,

Q: Use the Laplace transform to solve the initial-value problem y' + 3y = 13 sin2t, y(0) = 6

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

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Q: a) Use the method of Laplace transform to solve dx 10, dt given that x(0) = 4.

A: Since both the questions are different. So as per our guidelines, we are supposed to solve only…

Q: Use the Laplace transform to solve the given initial-value problem. y" - 3y' = 4e2t - 2e-t, y(0) =…

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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: 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)