Hi all,

I understand everything in the following example up until the words "Now, consider..."

http://s3.postimage.org/1qyo1zk04/qu...ar_example.jpg

Could somebody help me to understand how we get the part?

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- Dec 9th 2010, 01:59 AMfourierwarriorGeneral Solution of Quasilinear Equations
Hi all,

I understand everything in the following example up until the words "Now, consider..."

http://s3.postimage.org/1qyo1zk04/qu...ar_example.jpg

Could somebody help me to understand how we get the part? - Dec 9th 2010, 03:12 AMHallsofIvy
It's simply the product rule. You are differentiating with respect to s. Presumably, x and y are functions of s but u, here, is independent of s so we can treat it as a constant. The derivative of is .

- Dec 9th 2010, 04:52 AMfourierwarrior
Sorry, I should have mentioned that all 3 functions, x, y and u are functions of s here.

I understand the product rule, but I don't have a clue where the (x+u)/y sprung from.

My understanding of this problem is that we're trying to find two functions

= constant

= constant

as the solution of the equation satisfies = 0

Since = 0,

(x+u)/y is a constant, and so there's .

I just don't understand how we got there.

In the notes I have, there is alternative way of solving these quasilinear equations, which involves integrating the characteristic equations, then parametrising the initial line and setting s = 0. Does this sound familiar to anyone?