Trouble understanding solution to a PDE

Asked Sep 07 '20 at 01:43

Active Sep 07 '20 at 01:43

Viewed 32 times

So I was looking at this post, and I think I understand how most of the solution goes, but there's one line that's still pretty mysterious to me.

Under the second method that's presented, using characteristic curves, we see the implication $$y dy- x dx = 0 \implies d(y^2-x^2) = 0.$$

I was hoping someone could shed some light on 1) how this move is justified, and 2) why what the motivation is for taking this step?

asked Sep 07 '20 at 01:43

Bears

1

$d(y^2-x^2)=2ydy-2xdx$ – J. W. Tanner Sep 07 '20 at 01:45
1

Wow. That was way more straightforward than I thought.
I appreciate the help.
– Bears Sep 07 '20 at 01:46
are you familiar with exact differentials? – J. W. Tanner Sep 07 '20 at 01:50
Not really, no. I'm kind of learning on the fly, and so had assumed than much of the algebra being done with things of the form $du$ was justified through taking limits and linearity of the differential operator. – Bears Sep 07 '20 at 01:52

0 Answers0