zepdrix
  • zepdrix
Partial Differential Equations. First-Order Linear Equations.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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zepdrix
  • zepdrix
\[\Large 3u_y+u_{xy}=0\]Hint: let \(\large v=u_y\)
zepdrix
  • zepdrix
I've fallen a lil bit behind on my homework so I'm just getting a tad confused :) lol
zepdrix
  • zepdrix
Taking the derivative of the sub, \(\large v_x=u_{xy}\)

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zepdrix
  • zepdrix
\[\Large v_x+3v=0\]
zepdrix
  • zepdrix
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,\[\Large ve^{3x}=f(y)\]
zepdrix
  • zepdrix
\[\Large v=f(y)e^{-3x}\]Plugging u back in,\[\Large u_y=f(y)e^{-3x}\]Integrating with respect to y,\[\Large u=F(y)e^{-3x}\]
zepdrix
  • zepdrix
Something like that maybe? +_+ Grrr no answer key to check my work :c
zepdrix
  • zepdrix
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\[\Large u=F(y)e^{-3x}+g(x)\]
zepdrix
  • zepdrix
hmm

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