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    comiconor's Avatar
    comiconor Posts: 2, Reputation: 1
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    #1

    Jun 10, 2014, 12:40 PM
    First order differential equation, solving for y
    If I have an equation in the form: dy/dx + f(x)y = g(x)

    How can it be solved as y = e^-w * (integral (g(x)*e^w dx) + k) ?

    To make it simpler, g(x) = 0, which would make it:

    y = e^-w * k

    But I still don't see how you arrive at this formula.
    comiconor's Avatar
    comiconor Posts: 2, Reputation: 1
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    #2

    Jun 10, 2014, 12:41 PM
    Just to be clear, w = integral f(x) dx
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #3

    Jun 10, 2014, 12:58 PM
    Seems to work. If g(x) = 0 then:



    If , then substituting in the above yields:



    We can substitute for to get:

    , as expected.

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