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: 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: Write the ratio as a ratio of whole numbers using fractional notation 12 to 1

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Q: O For the differential equation -at y" + 2y'- 3y = 6e Determine the solutioo using Laplace t theorem…

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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: dx 4x = 2e2t + e4 dt

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Q: 2.x²y"+xy'–3y= 0,x>0

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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: Find Fourier sine transform of - and deduce that

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

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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: Solve the following DE using laplace transform method  y"-4y=0 when y(0)=0, y'(0)=6

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Q: How do I solve for the third order y''' - 4y''-11y' + 30y = 4e^8t + t^2 using the method of 1.…

A: repost the question for other method separately

Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

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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

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

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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: Solve using Laplace transform y" - y = e' cost, y(0)= 0, y'(0)=0

A: Solve the differential equation by using lapalce transformation

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

A: Given