Use the Laplace transform to solve the following initial value problem: y" + 8y' = 0 y(0) = 3, y'(0) = 8 %3D First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation Now solve for Y(s) = A and write the above answer in its partial fraction decomposition, Y(s) B where a < b sta s+b Y(s) = Now by inverting the transform, find y(t) =

Q: Using Laplace Transform method, solve the following differential equation with conditions y(0) =…

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A: Given solution is Ys = 5s2 +s -1s3 +9s  This can be written as Ys = 5s2 +s -1s s2 +9          = -19…

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Q: Now that we have figured out how to do step 1, we are going to try and do steps 1 and 2. Given the…

A: Given differential equation is y'' + 5y' + 3y = 0, with y(0) = 1, y'(0) = 0

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Q: Use the Laplace transform to solve the following initial value problem: (0) = 5, y(0) = -4 First,…

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Q: 6) Consider the differential equation y" – 2y' – 8y = 0. Solve this ODE using the Laplace transform…

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Q: 2.1 By applying Newton's second law to a body at a certain distance x at time t, the following…

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Q: Given the differential equation and its initial conditions y" + y' = 12 + 2 with y(0) = 1 and y'(0)…

A: Take the Laplace transform on both sides of the differential equation.

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Q: Given the differential equation y'' - 3y' - 4y = 0, y(0) = 2, y'(0) = -1 Apply the Laplace Transform…

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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: (6) Solve the Integro-differential equation: +4y +5 y(t) dt = e-t; y(0) = 0 dx (7) Find the Fourier…

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Q: Use the Laplace transform to solve the following initial value problem: y" +y + 2y = h(t - 4), y(0)…

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Q: Consider the following initial value problem: x" – 4x' – 21 sin(3t), x(0) = 7, x'(0) = 5. - Using X…

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Q: Q2) Given the differential equation d²x dx + 5. + 4x = 10 u(t) dt dt2 a) Find x(t) for the case that…

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Q: Consider the initial value problem y" + 16y= cos(4t), y(0) = 3, y'(0) = 8. a. Take the Laplace…

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Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the…

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Q: dy +4 dt -4w y(t - w) e dw = 8, y(0) = 0. a. Use convolution and Laplace transforms to find the…

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Q: Use the Laplace transform to solve the given differential equation subject to the indicated initial…

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Q: Given the differential equation y"+ 4y' + 2y = - 4 sin(4t), y(0) = - 1, y'(0) = 2 Apply the Laplace…

A: Given - Given the differential equation y'' + 4y' + 2y = -4sin4t,  y0 = -1, y'0 = 2 To find - Apply…

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Q: Use the Laplace transform to solve the following initial value problem: x' = 12x + 4y, y -8x + e¹t…

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Q: Consider the initial value problem y" + 4y = 12t, y(0) = 8, y (0) = 4. a. Take the Laplace transform…

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Q: 4. When solving a differential equation using the Laplace transform, you apply the Laplace transform…

A: We use Laplace transform formula to find Y(s).