# Toronto Math Forum

## APM346-2015F => APM346--Home Assignments => HA3 => Topic started by: Victor Ivrii on September 28, 2015, 01:03:59 PM

Title: HA3-P1
Post by: Victor Ivrii on September 28, 2015, 01:03:59 PM
http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter2/S2.3.P.html#problem-2.3.P.1 (http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter2/S2.3.P.html#problem-2.3.P.1)
Title: Re: HA3-P1
Post by: Zaihao Zhou 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.
Title: Re: HA3-P1
Post by: Gabriel Jacot 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.
Title: Re: HA3-P1
Post by: Yumeng Wang 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 ?
Title: Re: HA3-P1
Post by: Victor Ivrii 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.