Use the Laplace transform to solve the given initial value problem (y' = dy dt Y(s) = y" + 6y' +9y=0 y(0) = -3, y'(0) = 11 (-11 - 3s) S +65 +9 y(t) = -3e -3t X + 17 te -3s - 7 s² + 6s +9 -3t

Q: Use the Laplace transform to solve the initial value problem y' +4x²y = -28 -25 (t-1) +S(t-1), y(0)…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: Use Laplace transform technique to solve the initial value problem y" – 4y = e*, y(0) = 0, y'(0) =…

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Q: x2y3-y=x+x2 find dy/dt

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Q: y''+y'=0 where y(0)=0, y'(0)=1 laplace transform of derivatives

A: Given that:-  y" + y' = 0 and y(0)= 0, y'(0) =1 We find laplace transform of this differential…

Q: Solve the differential equation using the Laplace transform у" — 5y — бу %3Dеs", y(0) 3D 0; у' (0)…

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Q: (i) B(2,3)-

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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: ctan x (2) Let h(x) = t dt, calculate h'(T/3). ww. t2 + 2

A: Solve the following

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

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Q: Integrate (a) S2(* dt (b) S(x+1)³ dx (c) cos(-x)(x²)dx

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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: Laplace transform of x(t) = cos(4f)u(t) %3D 16 X (s) = s* +16 4 X (s) = s* +16 X(s)D s? +4 X(s) = s´…

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

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Q: Let F (x) = (1 + t2)/5 dt - Then F'(x) =

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Q: у" - 5у' + бу %3D7 УО) %3 2, у' (0) — 4

A: We use the following standard results to solve the given problem.…

Q: Find the general solution to the linear ODE. Use each method (integrating factors and educated…

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Q: Use the method of Laplace transforms to solve the symbolic initial value problem y" + 4y = 8(t – 3),…

A: The solution is given below

Q: Solve y(x) for the Second Order ODE in parameter form: y"+7y'+10y=6e^3x

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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: e 8(t – 3) dt = e^15 cos(31)6(t – 5) dt =

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Q: 5. dx/dt = (4+x)(y-x), dy/dt = (10-x)(y + x)

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Q: What is the valuea +b+e for Y()= + problem given by y"+ 7y'+ 6y -e', y(0) = 0, y (0) = 02 which is…

A: Given differential equation is y''+7y'+6y=-e-t, y(0)=0, y'(0)=0.

Q: e'dy + (5t + ye')dt = 0.

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