HA3-P1

[Victor Ivrii]

http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter2/S2.3.P.html#problem-2.3.P.1

[Zaihao Zhou]

General solution: \begin{equation} u = \phi(x+ct) + \psi(x-ct)     \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.

[Gabriel Jacot]

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

[Yumeng Wang]

Do we need to derive general solution for u_tt - c²u_xx = 0 during exam??
Or we can just use it directly ?

[Victor Ivrii]

Do we need to derive general solution for u_tt - c²u_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.