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Differential Equations

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Moderate

Solutions of ODEs Using Laplace Transforms 5

DIFFEQ-IXNKX2

Solve the IVP below using the Laplace Transforms:

$$y'-y=5\cos t, \ y(0)=1$$

A

$$y=2e^{-t} - (\sin t -\cos t)$$

B

$$y=(7/2) e^t +(5/2) (\sin t -\cos t)$$

C

$$y=(1/2) e^{5t} +(1/2) (\sin t -\cos t)$$

D

$$y=(11/2) e^t -(9/2) (\sin t -\cos t)$$