# Toronto Math Forum

## APM346-2016F => APM346--Lectures => Chapter 2 => Topic started by: ziyao hu on October 17, 2016, 06:15:10 PM

Title: HA #4 general
Post by: ziyao hu on October 17, 2016, 06:15:10 PM
I saw the solution professor posted last year, as the folloing picture.
Can we just assume constant = 0 and then put one at the end of the solution?
Title: Re: HA #4 general
Post by: Victor Ivrii on October 17, 2016, 10:42:24 PM
Can we just assume constant = 0 and then put one at the end of the solution?
No since in the different places this constant enters differently.

Title: Re: HA #4 general
Post by: ziyao hu on October 18, 2016, 07:05:46 PM
So what's the meaning of "up to constants that will not affect u(x,t)"
Title: Re: HA #4 general
Post by: Shentao YANG on October 18, 2016, 09:13:21 PM
I guess the meaning is: even if you take the constant as $0$ (which indeed should be $\pm {c \over 2}$ for some constant $c$), $u$ function you get will still satisfy the defining equations in the problem, hence, be a solution.
And, in fact, I think you will always get the same solution to $u$ for any integration constant you put (since the constant in $\psi$ and $\phi$ will cancel each other).
Title: Re: HA #4 general
Post by: Victor Ivrii on October 18, 2016, 09:31:54 PM
So what's the meaning of "up to constants that will not affect u(x,t)"

It should be in the context: $u(x,t)=\phi(x+ct)+\psi (x-ct)$; if we replace $\phi$ by $\phi+C$ and $\psi$ by $\psi-C$ then $u$ does not change