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Math Help - e^-x dy/dx = 1

  1. #1
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    e^-x dy/dx = 1

    Solve e^-x dy/dx = 1
    when y=5 and x = 0

    the solution I have been given is





    this is far I go before getting confused as the solution I have been given is wrong or else my methods are wrong. can some correct me please?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: e^-x dy/dx = 1

    Quote Originally Posted by decoy808 View Post
    Solve e^-x dy/dx = 1
    when y=5 and x = 0

    the solution I have been given is





    this is far I go before getting confused as the solution I have been given is wrong or else my methods are wrong. can some correct me please?

    e^{-x} \frac{dy}{dx}=1

    \frac{dy}{dx}=e^x

    dy=e^x{dx}

    \int dy=\int e^x{dx}

    y=e^x+C

    (0,5)

    5=e^0+C

    5=1+C

    C=4

    Hence:

    y=e^x+4
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  3. #3
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    e^(i*pi)'s Avatar
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    Re: e^-x dy/dx = 1

    Quote Originally Posted by decoy808 View Post
    Solve e^-x dy/dx = 1
    when y=5 and x = 0

    the solution I have been given is





    this is far I go before getting confused as the solution I have been given is wrong or else my methods are wrong. can some correct me please?
    You're integrating a term with x in as part of dy when it should be integrated with respect to x.

    Since this equation is separable it's much easier to multiply both sides by e^x


    e^{-x} \cdot e^x\ dy = e^{x} \ dx \ \Leftrightarrow \ dy = e^x\ dx


    Then proceed as per Also sprach Zarathustra's method
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