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Math Help - please help i need to work out the intial value problem

  1. #1
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    Smile please help i need to work out the intial value problem

    the derivate of y + y = 2 / (1+4e^2x)
    y(-ln2)=pi/2
    y=e^-x*tan^-1(2e^x)
    i need to find out the intial value plz someone help me work it out
    greatly appreciated

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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jam333 View Post
    the derivate of y + y = 2 / (1+4e^2x)
    y(-ln2)=pi/2
    y=e^-x*tan^-1(2e^x)
    i need to find out the intial value plz someone help me work it out
    greatly appreciated

    so nice of you to find the answer for us.

    anyway, here is how to continue (you forgot the arbitrary constant by the way)

    we have:

    y = e^{-x} \arctan (2 e^x) + Ce^{-x}

    we are told that:

    y(- \ln 2) = \frac {\pi}{2}

    this means:

    y(- \ln 2) = e^{ \ln 2} \arctan \left( \frac {2}{e^{\ln 2}} \right) + Ce^{\ln 2} = \frac {\pi}{2}

    \Rightarrow 2 \arctan(1) + 2C = \frac {\pi}{2}

    \Rightarrow 2 \cdot \frac {\pi}{4} + 2C = \frac {\pi}{2}

    \Rightarrow C = 0

    \Rightarrow y = e^{-x} \arctan (2 e^x)
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  3. #3
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    Thumbs up

    thanks helped me outalot
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