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Math Help - Integrating factos - first order DE

  1. #1
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    Integrating factos - first order DE

    Hi All,
    Could not solve this one: 12-x-3y+(x-y+4)y'=0 , y(0)=1
    I tried to find an integrating factor in order to make it an exact equation but did not succeed.
    would appreciate your help!
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  2. #2
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    Re: Integrating factos - first order DE

    Put the differential equation into standard form. then Begin to find the integrating factor.
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    Re: Integrating factos - first order DE

    If I understand correctly the standard form has to be: y' + P(x)*y=Q(x) and specifically: y'-3y/(x-y+4)=(x-12)/(x-y+4)
    but since there is a polynomial in the denominator of P(x) which includes y this is not the standard form.
    Right?
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  4. #4
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    Re: Integrating factos - first order DE

    I believe the standard form Cbarker was referring to is actually \displaystyle \begin{align*} f(x,y)\,dx + g(x,y)\,dy = C \end{align*}, which you can then find an integrating factor for to make the equation an exact equation.
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