# Toronto Math Forum

## APM346--2019 => APM346--Lectures & Home Assignments => Home Assignment 2 => Topic started by: Rhamel on January 15, 2019, 04:12:16 PM

Title: Home Assignment 2 problem 1(a)
Post by: Rhamel on January 15, 2019, 04:12:16 PM
For problem 1(a) equation 8: $u_t + (x^2+1)u_x = 0$

From solving for the characteristic equation I get $x = \tan(t-k)$ where k is a constant.

My question is how would I draw the characteristics in this case? The periodic nature of tan would result in just an indistinguishable blob of lines if I were to plot it out? Should I just draw the lines for one value of k?
Title: Re: Home Assignment 2 problem 1(a)
Post by: Victor Ivrii on January 15, 2019, 05:04:28 PM
You draw just a bit more than one period and say "$\pi$-periodic"