Solve each of the following by Laplace Transform: 1.) ď² y +2 + Y dy dt - = sinh 3t - 5 cosh 3t dt² y (0) = -2 y' (0) = 5 " d²y Y 4 dy dt - 5y = e-3t - sin(4t) 3 y' (0) 10 = 2.) dt² y (0) =

Q: Solve the following IVP by the Laplace transform. y(t) = = y" - 6y + 5y = 174 cos(2t), y(0) = 19.2,…

A: Given IVP y''-6y'+5y=174cos(2t), y(0)=19.2, y'(0)=37.2

Q: (x' = x- 2y V = 5x – yi x(0) = -1, y(0) = 2. %3D %3D %3D %3D

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Q: 7. Evaluate y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: Solve the following DE using Laplace Transform 3. y" - y' -2y = 5 sinx y(0) = 1, v'(0) = -1

A: The given differential equation .We have to solve the differential equation using the Laplace…

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: 7. Obtain the Fourier sine transform of the following functions: sin wx (c) x² +1' w > 0

A: The given problem is to find the Fourier sine transform of the given function, we have a general…

Q: dx 4x = 2e2t + e4 dt

A: NOTE: Refresh your page if you can't see any equations. .

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: Find Fourier sine transform of - and deduce that

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Q: c) Use a pair (table) to findz-transform of x(n) = 20.65 √2 cos((-)n-1.415)u(n)

A: Introduction: There are many properties that are followed by Z-transformation. It helps us to…

Q: y" + y' = t; y(0) = 1 , y'(0) = -2

A:

Q: Use Laplace transform technique to solve , y"-y'-6y= 0, Given y(0) = 1 and y'(0) = -1

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

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Q: 6. Evaluate * y" + 9y = 0; y(0) = 2 , y'(0) = 9 2cos3t + 3sin3t 2cos3t + 9sin3t C. A. 3(cos3t +…

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Q: Transform the differential equation 2y′′−y′+4y=e^(mt) y(0)= 2 y′=5 into an algebraic equation by…

A: (.) Given differential equation is ,           (.) Some properties of Laplace transform :-

Q: y" + 3y - 4y = 6e²t-3, y(1.5) = 4, y'(1.5) = 5

A:

Q: solve for Y(s), the Laplace transform of the solution y(t): y'' +6y'+5y=te^t  where y(0)=2 and…

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Q: Solve y"+y=2t, y 4)=(4)=2-√2 by using Laplace transform. of f/x)=1/x/x²2² +01 Find the courier Sine…

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Q: Find a 4th degree differential equation whose solution y(t) satisfies L{y(t)} = Y (s) = 1/ (s^4 +1)…

A: Formula for Laplace transformations L{0} = 0 L{a·f(t)+b·g(t)} = a·L{f(t)}+b·L{g(t)} here a and b are…

Q: (b) Use the Laplace transform method to find the solution of d²y 6+9y= 4e", yo = 2, y1 = 0. dt dy…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Q1) Solve the following equation with Laplace Transform Method (Inverse Laplace the equation to find…

A: Given differential equation is y''−3y'−4y=3e2x and y0=1 and y'0=0 Take Laplace transform of…

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

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Q: You can afford a $950 per month mortgage payment. You've found a 30 year loan at 7% interest…

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

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Q: What is the inverse Laplace transform of 1 /[(s-2) ^2 + 9]? C. 3e^ (-2t) D. 2 sin (2t) 5. A. sin…

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Q: Solve for the general and particular solution using Laplace Transform y" +y = sqrt (2) (cos sqrt…

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Q: Initially 80 grams of radioactive substance was present. After 2 hours the mass had decreased by 6%.…

A: By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

Q: Q1) Solve the Second Order Deferential Equation by using Laplace Transform. y" + 6y' + 8y = 0, y(0)…

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

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Q: 1) Solve U = Uz + U, u(1,t = 0) = sin(e¯² ) cos z, COS T, %3D %3D

A: Given,             and

Q: 1. (a) Solve the following equations by using Laplace transform; i.) d?x/dt² + 4 dx/dt + 3x = 2 x(0)…

A: Given