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Homework Help: First Order Differential (Just identify)

  1. Oct 22, 2008 #1
    Not sure if I should have put this here or in the homework section but I am simply asking for direction on these problems.

    I have 5 problems to work on and my biggest problem is identifying what method to use to find the answer. I don't need help answering because it's something I'd like to do myself but have some trouble with as I learn.


    Don't know how to use the neat forum stuff yet but will learn as I become part of the community slowly.

    Problems to work on...
    http://img261.imageshack.us/img261/9066/matwk8.jpg [Broken]

    Those are the problems and so far I can see...

    #1 ?
    #2 is a separable equation correct?
    #3 ?
    #4 is substitution and then exact?

    Already marked that one exact since I did it already.
    Can't tell which one would follow Bernoulli equation, integrating factor, linear first order.


    Thank you to anyone who would kindly reply :x


    Edit: Took a look at the rules again and see that this really should belong in the homework section. I'm very sorry, I'll ask an admin/mod to move it.
     
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Oct 23, 2008 #2

    tiny-tim

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    Welcome to PF!

    Hi Vathral! Welcome to PF! :smile:

    For #1, try the obvious substitution. :wink:
     
  4. Oct 23, 2008 #3
    [tex]x \frac{dy}{dx} - y = \frac{x^3}{y} e^y_x[/tex]

    So
    [tex]v = \frac{y}{x}[/tex]

    [tex]y = vx[/tex]

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

    [tex]\frac{dy}{dx} = v+x \frac{dv}{dx}[/tex]



    [tex]x [v + x\frac{dv}{dx}] - vx = \frac{x^2}{v} e^v[/tex]

    [tex]xv + x^2 \frac{dv}{dx} - vx = \frac{x^2}{v} e^v[/tex]

    [tex]x^2 \frac{dv}{dx} = \frac{x^2}{v} e^v[/tex]

    [tex]\frac{dv}{dx} = \frac{e^v}{v}[/tex]

    [tex]\frac{vdv}{e^v} = dx[/tex]

    [tex]\frac{-v-1}{e^v} = x + c[/tex]

    [tex] \frac{-\frac{y}{x}- 1)}{e^y_x} = x + c [/tex]

    [tex] - \frac{y}{x} - 1 = (x + c) e^y_x[/tex]

    [tex] -y - 1 * x^2 e^y_x + cxe^y_x[/tex]

    [tex] y = x^2 e^y_x+cxe^y_x[/tex]

    This is for #1 of course. Anyone see anything wrong with the final answer? Thank you for the identifying, would like to take these questions an extra step now.
     
  5. Oct 23, 2008 #4

    tiny-tim

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    Hi Vathral! :smile:

    Fine up until that line :smile:

    but what happened to the - 1 on the left? :redface:

    For question 3, the only problem is the mixed terms (mixed x and y) …

    so start by ignoring the 8x2dx, and try and turn the other two into an exact differential … and then put the 8x2dx back in, of course. :smile:
     
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