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Math Help - Simultaneous Differential Equations

  1. #1
    Junior Member
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    Simultaneous Differential Equations

    I'm trying to solve the system of equations:

    (tan 2x) g'(x) + 2g(x) = 0, f'(x)  - f(x) g(x)=0<br />

    I rearrange for g(x) in the second equation and substitute that into the first which after a little rearrangement gives:

    tan(2x)((-(f'(x))^2)/(f(x)) + f''(x)) + 2f'(x) = 0

    I tried to use the integrating factor method but I can't seem to get anything from it, any help please?
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  2. #2
    MHF Contributor
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    Hello kevinlightman
    Quote Originally Posted by kevinlightman View Post
    I'm trying to solve the system of equations:

    (tan 2x) g'(x) + 2g(x) = 0, f'(x)  - f(x) g(x)=0<br />

    I rearrange for g(x) in the second equation and substitute that into the first which after a little rearrangement gives:

    tan(2x)((-(f'(x))^2)/(f(x)) + f''(x)) + 2f'(x) = 0

    I tried to use the integrating factor method but I can't seem to get anything from it, any help please?
    If you use the integrating factor method on the first equation, the solution comes out as:
    g(x) = A\csc(2x)
    The second equation then becomes:
    f'(x)-A\csc(2x)f(x) = 0
    which again can be solved using the integrating factor, which turns out to be (\tan x ) ^{-A/2}. This gives:
    f(x) = B (\tan x) ^{A/2}
    Grandad
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