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Math Help - Solve dt/dx=(at+m)/(bt+j)

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    Solve dt/dx=(at+m)/(bt+j)

    how do I solve dt/dx=(at+m)/(bt+j) where a, b, m, and j are constants?

    I thought of using separable equations but then I got stuck.

    (So bt+j/at+m)dt=dx....
    Last edited by mr fantastic; April 10th 2011 at 10:46 PM. Reason: Re-titled, clarified DE.
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    Quote Originally Posted by Taurus3 View Post
    how do I solve dt/dx=(at+m)/(bt+j) where a, b, m, and j are constants?

    I thought of using separable equations but then I got stuck.

    (So bt+j/at+m)dt=dx....
    \displaystyle \frac{dt}{dx} = \frac{at + m}{bt + j}

    Basically you need to do the integral:
    \displaystyle \int \frac{bt + j}{at + m}~dt

    Split up the fraction:
    \displaystyle = \int \left ( \frac{bt}{at + m} + \frac{j}{at + m} \right ) dt

    \displaystyle = \frac{b}{a} \int \frac{t}{t + \frac{m}{a}} dt + \frac{j}{a} \int \frac{1}{t + \frac{m}{a}} dt

    Can you take it from here?

    -Dan
    Last edited by mr fantastic; April 10th 2011 at 10:48 PM. Reason: I clarified the OP's equation.
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    ummm.....it's still a bit confusing of how you do the integrals with all those different constants...
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  4. #4
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    Quote Originally Posted by Taurus3 View Post
    ummm.....it's still a bit confusing of how you do the integrals with all those different constants...
    Then make the integrals like simpler by substituting \displaystyle k = \frac{m}{a}. If you're studying differential equations you're expected to know how to integrate!

    If you need more help please show all your working and say where you are stuck.
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