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Math Help - 1st order Differential Equation -exact

  1. #1
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    1st order Differential Equation -exact

    Hi,

    I would like to know how do I show that:
    y-(e^x) cos y + [x+(e^x) sin y]y' = 0 is an exact differential equation.
    Thanks in advance.
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  2. #2
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    Quote Originally Posted by zxcv View Post
    Hi,

    I would like to know how do I show that:
    y-(e^x) cos y + [x+(e^x) sin y]y' = 0 is an exact differential equation.
    Thanks in advance.
    Read this: Exact differential - Wikipedia, the free encyclopedia

    You have (y - e^x \cos y) \, dx + (x + e^x \sin y) \, dy = 0

    where A = y - e^x \cos y and B = x + e^x \sin y.

    Show \frac{\partial A}{\partial y} = \frac{\partial B}{\partial x}.
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