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Find the solution of this differential equation

  • Thread starter supercali
  • Start date
  • #1
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Homework Statement



if
[tex]f \left( x,y \right) =xy*g \left( 7\,{x}^{2}-9\,{y}^{2} \right)[/tex]
then the differential equation [tex]9y\frac{{\partial f}}{{\partial x}} + 7x\frac{{\partial f}}{{\partial y}} = ?[/tex] is equal to?

Homework Equations


--


The Attempt at a Solution


i triedto do a partial derivatives wich doesnt really seem to work
if you can just give me a direction in which to go to
thanks
 

Answers and Replies

  • #2
tiny-tim
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i triedto do a partial derivatives which doesnt really seem to work
Hi supercali! :smile:

I don't see what doesn't really seem to work … which might be because you haven't told us! :rolleyes:

(you do know they don't want you to solve the equation, only to write it out?)
 
  • #3
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i dont think i really understand what it is i need to do
 
  • #4
tiny-tim
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Just write out ∂f/∂x, and multiply it by 9y … :smile:

(they haven't told you what g' is, so just leave it as g')

(you do understand that g is an ordinary function, don't you?)
 
  • #5
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no thats not what they want me to do
they want me to form a differential equation the answer suppose to be with f ,x and y
but i just dont think i understand how to do so
 
  • #6
378
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Find
1. df/dx
df/dy

g(mess) is a function, so use chain rule for it

2. Substitute df/dx and df/dy in your target equation

I think you misunderstood tiny-tim. You don't write out but do substitution.

You don't need anything else (I can say for sure :) )
 
  • #7
tiny-tim
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Hi supercali! :smile:

they want me to form a differential equation the answer suppose to be with f ,x and y
No … they want you to form a differential equation with g x and y.

f should disappear :smile:
 
  • #8
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now i have the question infront of me the say there that they want the answer in terms of y x and f not g
 
  • #9
tiny-tim
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now i have the question infront of me the say there that they want the answer in terms of y x and f not g
no wonder you're confused …

once you've done ∂/∂x to f, the f has gone!

all that's left is x and y and g and g'

Anyway, as rootX says, just work your way through it! :smile:
 
  • #10
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solution:derive f
[tex]9\,y \left( yg \left( 7\,{x}^{2}-9\,{y}^{2} \right) +14\,{x}^{2}y
\mbox {D} \left( g \right) \left( 7\,{x}^{2}-9\,{y}^{2} \right)
\right) +7\,x \left( xg \left( 7\,{x}^{2}-9\,{y}^{2} \right) -18\,x{y
}^{2}\mbox {D} \left( g \right) \left( 7\,{x}^{2}-9\,{y}^{2} \right)
\right) [/tex]
gives:
[tex]9\,{y}^{2}g \left( 7\,{x}^{2}-9\,{y}^{2} \right) +7\,{x}^{2}g \left( 7
\,{x}^{2}-9\,{y}^{2} \right)[/tex]
since [tex]f= xyg \left( 7\,{x}^{2}-9\,{y}^{2} \right)[/tex]
we can get an expretion for y*g and x*g thus the final answer is
[tex]9\,{\frac {yf}{x}}+7\,{\frac {xf}{y}} [/tex]

thanks for all the help
 

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