Toronto Math Forum

APM346-2012 => APM346 Math => Home Assignment X => Topic started by: Aida Razi on October 15, 2012, 01:34:28 AM

Title: Problem2
Post by: Aida Razi on October 15, 2012, 01:34:28 AM

Solution is attached,

Title: Re: Problem2
Post by: Thomas Nutz on October 15, 2012, 12:04:21 PM

I obtain the solution
$$
u(x,t)=\frac{1}{2}((x-ct)e^{x+ct}+(x-ct)e^{x-ct})+
\int_{x-ct}^{x+ct}e^{-x}dx+\int_0^{t}\int_{x-ct}^{x+ct}e^{-x-t}dxdt
$$
which becomes
$$
\frac{2ce^{-x}}{1-c^2}+\frac{e^{-t}(e^{-ct}+e^{ct})}{1+c}
$$
(plugging in $c=5$ doesn't really simplify it)

Did anyone get the same?

Title: Re: Problem2
Post by: Victor Ivrii on October 15, 2012, 12:53:20 PM

Thomas,

I fixed you LaTeX (it was a double subscript error \int_{0{}_{t} but your formula is wrong: you should integrate by $x$ (inner) from $x-c(t-s)$ to $x+c(t-s)$ and integrand is $e^{x-s}$ and then you integrate by $s$ from $0$ to $t$; also forgot $\frac{1}{2c}$ factor.

I have not checked other terms. You can see that your "solution" does not satisfy initial conditions (or equations)

Title: Re: Problem2
Post by: Betty Zhu on October 15, 2012, 04:03:18 PM

Razi, I agree with you, I got the same answer....hope it is the correct one...