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Math Help - Differential equation

  1. #1
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    Differential equation

    Hi, I'm having problems with the following differential equation:

    \frac{dy}{dx}=\frac{1}{y}-\frac{3}{4}

    Have you got any ideas?
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  2. #2
    Senior Member Peritus's Avatar
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    sure, I have a pretty good idea.
    first you rearrange the equation like so:

    <br />
\frac{{4y}}<br />
{{4 - 3y}}dy = dx<br />

    so this is basically a separable equation, all you have to do now is to integrate both sides.

    <br />
y + \frac{4}<br />
{3}\ln \left| {4 - 3y} \right| =  - \frac{3}<br />
{4}x + C<br />

    I doubt that an explicit form of the solution can be obtained.
    Last edited by Peritus; September 20th 2008 at 06:51 AM.
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  3. #3
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    Quote Originally Posted by Aliquantus View Post
    Hi, I'm having problems with the following differential equation:

    \frac{dy}{dx}=\frac{1}{y}-\frac{3}{4}

    Have you got any ideas?
    How about separating variables:

    \frac{4ydy}{4-3y}=dx

    Hey, I think that turns into an interesting problem: Express the solution as y=f(x).
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  4. #4
    Senior Member polymerase's Avatar
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    You have to seperate the two variables such that all the y's are on one side and all the x's are on the other....so use cross multiplication...you should end up with this:
    \frac{4y}{4-3y}\;dy=dx
    Then you integrate both sides: 4\int\frac{y}{4-3y}\;dy=\int dx

    Make the substitution u=4-3y...rest follows

    Should end up with this: \frac{4}{3}(4-3y)-\frac{8}{3}\ln{|4-3y|}=x+C
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