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Multivariable Calculus

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Determine the Solution for the Boundary Value Problem

MVCALC-NGVCWJ

Determine the solution for the boundary value problem:

$$y'' + y = 4\cos t + 4t\sin t$$
$$y(0) = 5$$
$$y(\pi/2) = 2\pi$$

A

$y(t) = 5 \cos t + 2\pi \sin t$

B

$y(t) = 5 \cos t + \pi \sin t + 2t\sin t - 3t\cos t$

C

$y(t) = 5 \cos t + \frac{\pi}{2} \sin t + 3t\sin t - t^2\cos t$

D

$y(t) = 5 \cos t + 2\pi \sin t + 3t\sin t - t^2\cos t$

E

None of the Above