By LAPLACE TRANSFORM METHOD, solve step by step the IVP a" + 6x' + 8x = 2sin (2t) , x (0) = 0, x' (0) = 1.

Q: Q"+4Q'+4Q=2t Solve with Laplace transform

A: Using laplace transform to solve the problem.

Q: 1. f(t) = 5(e^-4t)[cos(10t)] A. (5s – 20) / (s^2 - 8s + 116) B. (s - 4) / (s^2 - 8s + 116) C. 50 /…

A: Laplace transferom of the function

Q: use laplace transform to solve y'-y=2cos(t), y(0) = 4

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Q: 4s 4 2-¹ (1-16) - O (5/2) e^(-4t)+(3/2) e^2t O None of them O (5/2) e^(-4t)+(3/2) e^4t (5/2)…

A: The given inverse Laplace transform .We have to find the inverse Laplace transform.

Q: use the laplace transform to solve the initial value problem y''- 4y'- 4y = t^3          y(0) = 1,…

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Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

Q: Consider the following IVP: y''-3y'-10 y=1, y(0)=-1,y'(0)=2 (a) Find the Laplace transform of the…

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Q: - y"+10y'+25y=0y(0)=0_y"(0) = 10

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: 4. f(t) = e^(5t)(t^3) A. 6/ (s-5)^4 B. 6/ (s+5)^4 C. 6/ (s-5)^3 D. 6/ (s+5)^3 %3D

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Q: Laplace Transform. Please show your complete solution

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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: Let A, B be two square matrices, then mark all correct answers a. A°=1 O b. (AB)"= BTAT O c. (AT+…

A: Correct answers are:  a, b, c, e, f.

Q: 8.(a) Find the Fourier transform for the function cos x, -n/2 7/2 f(x) = 0, (b) Use the result in…

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Q: Use the laplace transform to solve 3x'-y=2r;x'+y'-y=0; x(0)=y(0)=0

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Q: 2. y" – 2y' = -4 y(0) = 0, y'(0) = 4

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Q: 3. f(t) = [sin(2t)]^2 %3D

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Q: 6) Use a Laplace Transform to solve. y(4) - 4y(3) + 6y" -4y' + y = 0; y(0) = 0, y'(0) = 1, y"(0) =…

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Q: 3. State and explain the Convolution Theorem for Laplace transform

A: We have to state and proof  the convolution theorem of laplace transform.

Q: Solve the shifted data IVP by the Laplace transform method showing your work in details.…

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Q: Use Laplace transform to solve the following IVP y′′(t) = 4y(t) −e^(−t)U(t −1), y(0) = y′(0) = 0.

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Q: Use the Laplace transform to solve the initial value problem: 2y" + 3y' - 2y = te-²t, y(0) = 0,…

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Q: y"+2"-z' = 0 y' + z 221-ex - Yo = 0, y = 1 20= 1, 2 = 1

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Q: 4. Solve the following initial value problems using the Laplace transform: a) y' + 3y = 0, y(0) =…

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Q: Use the laplace transform to solve 3r'-y=21;x'+y'-y=0; x(0)=y(0)=0

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Q: Use the Fourier transform method to solve du k at ax2-Yu, -o∞ 0 u(x, 0) = f(x).

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Q: 7. Find the Inverse Laplace Transform of 3/ sqrt [(s - 2)^3] * A. (6/T) [ t^(1/2) e^2t] B. (6/T^1/2…

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Q: Solve the IVP y""+y'=e*, y(0) = y'(0) = y" (0) = 0 using Laplace transform.

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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: What is the Fourier transform of 8(x) dx F(k) = 100 = 2T -ikx 8(x) =?

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

Q: When the Laplace transform is used to solve the IVP: y' +5 y=314, y(0) = 2 1/4+ the following…

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Q: A point (x,y)=(3,4) is transformerd. First with: [2 And then with: [29] Please calculate the result…

A: Given that , Point x,y=3,4 find the transformed point.

Q: In a well-written paragraph, explain the method of solving a differential equation using Laplace…

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Q: Use Laplace Transform to solve the given Initial Value Problem.  y''+9y=cos(3t)  y(0)=2 y'(0)=5

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Q: Use Laplace Transform to find the solution of the IVP 1. y"-10y'+9y=5t ---y(0) and y'(0)=2

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