### Author Topic: HA3-P1  (Read 2866 times)

#### Victor Ivrii

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##### HA3-P1
« on: September 28, 2015, 01:03:59 PM »

#### Zaihao Zhou

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##### Re: HA3-P1
« Reply #1 on: October 03, 2015, 01:16:22 PM »
General solution: $$u = \phi(x+ct) + \psi(x-ct)$$ for general form $$u_{tt} - c^{2}u_{xx} = 0$$
All of the equations in this question satisfy this general form with c=1, 2, 3, 1/2, 3 (possible mistake of the question, should put 9 in front of the first term, if so c = 1/3).
plug the corresponding c into the general solution we have the answer for each equation.

#### Gabriel Jacot

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##### Re: HA3-P1
« Reply #2 on: October 03, 2015, 01:36:29 PM »
I believe that there is a mistake in this question. Equation (3) is the same as equation (5). Please verify this.

#### Yumeng Wang

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##### Re: HA3-P1
« Reply #3 on: October 03, 2015, 06:21:10 PM »
Do we need to derive general solution for utt - c2uxx = 0 during exam??
Or we can just use it directly ?

#### Victor Ivrii

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##### Re: HA3-P1
« Reply #4 on: October 04, 2015, 04:06:15 PM »
Do we need to derive general solution for utt - c2uxx = 0 during exam??
Or we can just use it directly ?

No, you may use any formula you want. Solution of  Zaihao Zhou is perfect -- except in the Quiz if this problem is chosen you use the given value

PS. Don't use html tags for equations. Use MathJax with LaTeX syntax

Basically the exact value of $c>0$ does not matter in this problem.
« Last Edit: October 04, 2015, 04:09:00 PM by Victor Ivrii »