Consider the following initial value problem: 0≤t≤5 y" + 64y = 5t, 25, t>5 3(0) = 0, 3/(0) = 0 Using Y for the Laplace transform of y(t), i.e., Y = C{y(t)}. find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) =

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Q: Use the Laplace transform to solve the given initial-value problem. y' + 5y = e3t, y(0) = 2

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Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

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A: Given IVP y''-5y'=f(t)  , y(0)=1 , y'(0)=-1L(f(t))=8s-4-4s+1

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A: See the detailed solution below.

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A: Calculated integration and the applied laplace transformation in both sides

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Q: y" +16y= cos(41) 7. Solve the initial value problem (0) =1 (0)=1 using the Laplace transform. No…

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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: Determine the Laplace transform of the differential equation. y² + 4y y (0) = 0 = Cost;

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Q: Solve de next differential equation using the lapace transform   y´+ y = sin t + cos 2t

A: Take the Laplace transform, term by term:

Q: olve using Laplace Transform y" +5y -y=e' – 1, y(0)=1, y(0)=1

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