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Math Help - differential equations first order

  1. #1
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    differential equations first order

    dy/dx = xy^2/x+5


    how do I algebraically convert this into the form y/x
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  2. #2
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    Re: differential equations first order

    Quote Originally Posted by Dfaulk044 View Post
    dy/dx = xy^2/x+5


    how do I algebraically convert this into the form y/x
    I'm not really sure what you are asking here. You aren't going to be able to express this as f(y/x).

    The method you would use to solve this is called separation of variables.

    \frac{\text{dy}}{\text{dx}}=\frac{x y^2}{x+5}

    \frac{\text{dy}}{y^2}=\frac{\text{dx} x}{x+5}

    And you integrate on both sides to obtain your solution. You should be able to do this. Post back if you need more help.
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  3. #3
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    Re: differential equations first order

    is the answer -y^-1 = ln[x+5]
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  4. #4
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    Re: differential equations first order

    Quote Originally Posted by Dfaulk044 View Post
    is the answer -y^-1 = ln[x+5]
    It's not hard to check it. The derivative of the left side, with respect to x, is y^{-2} dy/dx and the derivative of the right side is 1/(x+ 5).
    So y^{-2} dy/dx= 1/(x+ 5) so dy/dx= y^2/(x+ 5).

    I do NOT see an "x" in the numerator on the right.

    The integral of x/(x+ 5) is NOT ln(x+ 5). If you need to, make the substitution u= x+ 5 so that x= u- 5 and \frac{x}{x+ 5}= \frac{u- 5}{u}= 1- \frac{1}{u}.
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