Question

Partial Differential Equations.
First-Order Linear Equations.

Answer 1

\[\Large 3u_y+u_{xy}=0\]Hint: let \(\large v=u_y\)

Answer 2

I've fallen a lil bit behind on my homework so I'm just getting a tad confused :) lol

Answer 3

Taking the derivative of the sub, \(\large v_x=u_{xy}\)

Answer 4

\[\Large v_x+3v=0\]

Answer 5

Then maybeeeeee integrating factor from here?\[\Large \mu=e^{3x}\]

\[\Large \frac{\partial}{\partial x}\left(ve^{ex}\right)=0\]Integrating with respect to x,\[\Large ve^{3x}=f(y)\]

Answer 6

\[\Large v=f(y)e^{-3x}\]Plugging u back in,\[\Large u_y=f(y)e^{-3x}\]Integrating with respect to y,\[\Large u=F(y)e^{-3x}\]

Answer 7

Something like that maybe? +_+
Grrr no answer key to check my work :c

Answer 8

Err when I integrate the second time, it's with respect to y, so I guess I should have a function of x popping up in place of my constant right? :o\[\Large u=F(y)e^{-3x}+g(x)\]

Answer 9

hmm