### Author Topic: Day Section Problem 2  (Read 3021 times)

#### Victor Ivrii

• Elder Member
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##### Day Section Problem 2
« on: February 27, 2013, 07:46:41 PM »
Post problem and solution

#### Changyu Li

• Full Member
• Posts: 16
• Karma: 10
##### Re: Day Section Problem 2
« Reply #1 on: February 27, 2013, 09:17:36 PM »
I think the question was
$$y'''-y= 2 \sin t$$
solution:
$$r^3 - 1 = 0 \\ (r+1)(r^2+r+1) = 0\\ r = -1, \frac{-1 \pm \sqrt{3} i}{2}\\ y_h = c_1 e^{-t} + c_2 e^{ \frac{-1 +\sqrt{3} i}{2}t} + c_3 e^{ \frac{-1 - \sqrt{3} i}{2}t} \\ y_p = A \sin t + B \cos t \\ y_p' = A \cos t - B \sin t \\ y_p'' = -A \sin t - B \cos t \\ y_p''' = - A \cos t + B \sin t \\ A = -1, B = 1\\ y = c_1 e^{-t} + c_2 e^{ \frac{-1 +\sqrt{3} i}{2}t} + c_3 e^{ \frac{-1 - \sqrt{3} i}{2}t} + \cos t - \sin t$$
« Last Edit: February 28, 2013, 02:03:43 AM by Victor Ivrii »

#### Jason Hamilton

• Jr. Member
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##### Re: Day Section Problem 2
« Reply #2 on: February 27, 2013, 10:09:57 PM »
NVM
« Last Edit: February 28, 2013, 01:02:09 PM by Jason Hamilton »