Toronto Math Forum
APM3462015F => APM346Home Assignments => HA3 => Topic started by: Victor Ivrii on September 28, 2015, 01:03:59 PM

http://www.math.toronto.edu/courses/apm346h1/20159/PDEtextbook/Chapter2/S2.3.P.html#problem2.3.P.1 (http://www.math.toronto.edu/courses/apm346h1/20159/PDEtextbook/Chapter2/S2.3.P.html#problem2.3.P.1)

General solution: \begin{equation} u = \phi(x+ct) + \psi(xct) \end{equation} for general form \begin{equation} u_{tt}  c^{2}u_{xx} = 0 \end{equation}
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.

I believe that there is a mistake in this question. Equation (3) is the same as equation (5). Please verify this.

Do we need to derive general solution for u_{tt}  c^{2}u_{xx} = 0 during exam??
Or we can just use it directly ?

Do we need to derive general solution for u_{tt}  c^{2}u_{xx} = 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.