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Math Help - Separable Differential Equation Question

  1. #1
    s3a
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    Separable Differential Equation Question

    Question:
    Solve the separable differential equation for
    Use the following initial condition: .
    ?

    My work:
    (Attached)

    Any help would be greatly appreciated!
    Thanks in advance!
    Attached Thumbnails Attached Thumbnails Separable Differential Equation Question-mywork.jpg  
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  2. #2
    Master Of Puppets
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    Quote Originally Posted by s3a View Post
    Question:



    Solve the separable differential equation for



    Use the following initial condition: .
    ?

    My work:
    (Attached)Any help would be greatly appreciated!
    Thanks in advance!
    \frac{du}{dt} = e^{4u+8t} = e^{4u}\times e^{8t},u(0)=-6

    Therefore

    e^{-4u}~du= e^{8t}~dt

    \frac{-1}{4}e^{-4u}= \frac{1}{8}e^{8t}+C

    e^{-4u}= \frac{-1}{2}e^{8t}+C

    -4u= \ln(\frac{-1}{2}e^{8t}+C)

    u= \frac{-1}{4}\ln(\frac{-1}{2}e^{8t}+C)
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