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Differential equation

  1. Dec 7, 2004 #1
    somebody slove this differential equations

    1/y' = (1/y)+(1/x)

    thanx in advance
     
  2. jcsd
  3. Dec 7, 2004 #2

    Zurtex

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    Perhaps looking at it like this:

    [tex]\frac{1}{\frac{dy}{dx}} = \frac{1}{y} + \frac{1}{x}[/tex]

    [tex]\frac{dx}{dy} = \frac{1}{y} + \frac{1}{x}[/tex]

    [tex]x\frac{dx}{dy} = \frac{x}{y} + 1[/tex]

    lol, I'll stop there because I suddenly realise this is beyond me (but it looks in a 'nicer' form, perhaps it will help you)
     
  4. Dec 7, 2004 #3
    Your solution is just a peanut compared to where i have gone....there is still more to go...anyhow thanx for trying,do try nmore and figure out the solution.

    regards
    drdolittle
     
  5. Dec 7, 2004 #4

    Zurtex

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    Well can you post what you have done please so others can help.
     
  6. Dec 7, 2004 #5

    Zurtex

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    I ran this through Mathematica: DSolve[1/(y'[x]) == 1/x + 1/y[x], y[x], x]

    And it gave me nothing sorry.

    Edit: Although I'm not used to using Mathematica and have yet to get it to solve the simplest thing I think I have inputed it right.
     
    Last edited: Dec 7, 2004
  7. Dec 7, 2004 #6
    try seperation of variables...after that iam struggling to cotinue....
     
  8. Dec 7, 2004 #7
    Even though I just started learning differential equations, I thought I'd give this a try:

    [tex]\frac{dx}{dy}=\frac{1}{y}+\frac{1}{x}[/tex]

    [tex]\frac{dy}{dx}=\frac{xy}{x+y}[/tex]

    [tex]x\frac{dy}{dx}+y\frac{dy}{dx}=xy[/tex]

    [tex]y+x\frac{dy}{dx}+y\frac{dy}{dx}=y+xy[/tex]

    [tex]\frac{d(xy)}{dx}+\frac{1}{2}\frac{d(y^2)}{dx}=y(1+x)[/tex]

    [tex]\frac{1}{y}\,d(xy)+\frac{1}{2y}\,d(y^2)=(1+x)\,dx[/tex]

    I don't know what to do now, and I don't know if any of this is right, but I hope it'd be of some use.
     
  9. Dec 8, 2004 #8

    Zurtex

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    Err I still think this is beyond me but I think you made a mistake on the LHS going from the 4th to the 5th line as:

    [tex]\frac{d(xy)}{dx} = x\frac{dy}{dx} + y[/tex]
     
  10. Dec 8, 2004 #9
    I added a y to the LHS in the 4th step.
     
  11. Dec 8, 2004 #10

    Integral

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    What I see when I look at that equation is a family of hyperbolas very much like the simple lens equation. There is a change of variables and a rotation that will reduce this equation to something which may be separable. Unfortunately I do not have the time to do all of the algebra for you.

    Explore doing a change of variables, perhaps to polar coordinates, see what you get.
     
  12. Dec 13, 2004 #11
    How do you guys write the nice format of dy/dx and the fractions? Which program do you use, and you post them as photos?

    I'll help in solving it, but after knowing how to post a math solution :wink:
     
  13. Dec 13, 2004 #12
    They use LaTeX. See this thread for more info :smile:.
     
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