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Math Help - Solve the following ODE .. #4

  1. #1
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    Solve the following ODE .. #4

    Problem:
    Solve the following equation:

    (1+e^y \cdot e^{\left( e^x \right)}) dx - dy = 0

    Solution:
    I multiply the equation by e^x, to get:

    (e^x+e^y \, e^x \cdot e^{\left( e^x \right)}) dx - e^x dy = 0

    e^xdx + e^y e^x e^{\left( e^x \right)} dx - e^x dy = 0

    Let t=e^x \implies dt=e^xdx

    the equation will be:

    dt+e^ye^tdt-tdy=0

    Now, I stopped!
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  2. #2
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    Multipy by e^{-y}.  It should be exact then.
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  3. #3
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    Thanks.
    I forgot the method of determinating the integrating factor .
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