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Differential equation help

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that the equation [tex]-\frac{x}{2}\frac{dy}{dx} = \frac{d^2y}{dx^2}[/tex]

    can be written as

    [tex]\frac{d}{dx}\left({\ln \frac{dy}{dx}}\right) = -\frac{x}{2}[/tex]

    3. Attempt at the solution

    I approached this by writing [tex]\frac{d}{dx}\left({\frac{dy}{dx}}\right) = -\frac{x}{2}[/tex]

    But this isn't the required result and I can't see how to get there?

    Please help!

    With very many thanks,

    Froskoy.
     
  2. jcsd
  3. Jan 30, 2012 #2

    Char. Limit

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    Gold Member

    As you know, if y = y(x), then d/dx ln(y) = y'/y. Thusly, dividing both sides by dy/dx gives you a very similar-looking form on the right side, which you should be able to solve from there.
     
  4. Jan 30, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    How could you get from an equation that involves ln to one that does not but everything else is the same? You can't just erase the letters "ln"!

    If you let u= dy/dx, this becomes the first order equation
    [tex]-\frac{x}{2}u= \frac{du}{dx}[/tex]
    Can you solve that equation?

    Once you know u, how do you find y?
     
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