Solve the following differential equations d’x +12y +6x = 0 dt dt? %3D +16dy dt? di? +6y=D0

Q: y" + 4y' + 3y = x² Solve this equation using Laplace transform

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Q: Use the Laplace transform to solve the following initial-value problem for a first-order equation.…

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Q: Find what m equals given tyll-3kyloMyo the differential equation

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

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Q: using Laplace transform. S=10h 'T=coh Ft = ht+by - banjos (8)

A: The given differential equation is:y''-4y'+4y=4cos2t;  y0=2,  y'0=5. We have to solve using Laplace…

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

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Q: y''+9y=10e-t,y(0)=0,y'(0)=0 by laplace transform

A: The objective of this question is to solve the given second order differential equation using…

Q: 4. (20 points) Use the Laplace Transform to solve the IVP y' +2y 2e", y(0) = 3

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Q: tan x If h(x) Vt + vt dt, then find ht(x). 0,

A: We apply here Leibniz rule

Q: Let Y(s) be the Laplace transform of y(t). Find the equation satisfied by Y(s) when solving the…

A: Introduction: The Laplace transformation is a very important tool in solving an initial value…

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

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Q: y'' + 4y = cos2t y(0) = -2 and y'(0) = 0 Solve the IVP using the Laplace Transform.

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Q: What is the smallest number that can be represented as the sum of four positive squares (not…

A: Consider the given statement. Since we need to find a number, which is the smallest number of sum of…

Q: y''-3y'+10y=e-2t , y(0) =0, y'(0)=1

A: We have to solve given problem:

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 = sin(2t) where y(0) = 2…

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Q: Using Laplace transform, solve y"+25y=t, y(0)=1 and y'(0)=0.04

A: Given that, y''+25y=t, y(0)=1, y'(0)=0.04 The laplace transform for, Ly''=s2y(s)-sy(0)-y'(0)Lt=1s2…

Q: Use the Laplace transform to solve y' - v = te'sint, y(0) = 0

A: To solve the given IVP, first we take the Laplace transform of differential equation and then we use…

Q: find

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