(1 point) Find y as a function of t if8y" + 27y = 0,y(0) = 2, y'(0) = 7.y(t)Note: This particular weBWorK problem can't handle complex numbers, so write your answer in terms of sines and cosines, rather than using e to a complex power.

Name: (1 point) Find y as a function of t if8y" + 27y = 0,y(0) = 2, y'(0) =
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Description: (1 point) Find y as a function of t if8y" + 27y = 0,y(0) = 2, y'(0) = 7.y(t)Note: This particular weBWorK problem can't handle complex numbers, so write your answer in terms of sines and cosines, rather than using e to a complex power.

Answered: (1 point) Find y as a function of t if…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(1 point) Find y as a function of t if
8y" + 27y = 0,
y(0) = 2, y'(0) = 7.
y(t)
Note: This particular weBWorK problem can't handle complex numbers, so write your answer in terms of sines and cosines, rather than using e to a complex power.

Expert Solution

Procedure:

Since the given differential equation is a second-order linear homogeneous ODE.

Therefore, we solve this differential equation by substituting $y = e^{r t}$ .

After solving the equation $e^{r t} (8 r^{2} + 27) = 0$ for r, and using initial conditions in the general solution of the differential equation, we get

$y (t) = 2 \cos (\frac{3 \sqrt{3}}{2 \sqrt{2}} t) + \frac{14 \sqrt{2}}{3 \sqrt{3}} \sin (\frac{3 \sqrt{3}}{2 \sqrt{2}} t)$ .

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