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Thread: 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?

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

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

    $\displaystyle dy=e^x{dx}$

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

    $\displaystyle y=e^x+C$

    $\displaystyle (0,5)$

    $\displaystyle 5=e^0+C$

    $\displaystyle 5=1+C$

    $\displaystyle C=4$

    Hence:

    $\displaystyle y=e^x+4$
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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 $\displaystyle e^x$


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


    Then proceed as per Also sprach Zarathustra's method
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