I have an equation $u_y - u_x^3 =0$, but because it's non-linear in a broader $F(x,y,z,p,q)$ case with $u_x=p, u_y=q$, I can't rely on the typical characteristic equations in the simpler linear case. But as far as I can tell, there is some kind of comparable technique I can use, but what exactly?
Asked
Active
Viewed 38 times
0
-
Separation of variables maybe works?! – K.K.McDonald Feb 29 '20 at 19:31
-
Look at the Lagrange-Charpit equations. A similar question is asked here. – Axion004 Feb 29 '20 at 20:51
-
In the LC equations, what is "s"? Is it actually supposed to be $t$ as in the other characteristic equations? Or is it supposed to be $s$ for arclength? – RandomWordMashup Feb 29 '20 at 21:00
-
I was expecting $$\frac{dz}{dt} = p\frac{dx}{dt} + q\frac{dy}{dt},$$ but maybe that is the wrong equation. – RandomWordMashup Feb 29 '20 at 21:01
-
How did they get $\frac{dx}{3p^2}$? I mean it looks like $F_p$ but how did they know how to do that? The characteristic looking equations in the book I'm reading are more complicated than that. – RandomWordMashup Feb 29 '20 at 21:08