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Math Help - Coupled differential equations

  1. #1
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    Coupled differential equations

    Anyone know how to solve these equations without using eigenvalues/eigenvectors?
    Can these be solved using standard integration techniques?

    dx/dt = 4x+2y
    dy/dt = -x +y where x and y are functions of t.
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  2. #2
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    Re: Coupled differential equations

    \frac{d^{\, 2}x}{dt^{2}}=4\frac{dx}{dt}+2\frac{dy}{dt} =  4\frac{dx}{dt}-2x+2y  =  4\frac{dx}{dt}-2x+\left(\frac{dx}{dt}-4x\right)

    so

    \frac{d^{\, 2}x}{dt^{2}} - 5\frac{dx}{dt}+6x = 0, etc.
    Thanks from MarkFL
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  3. #3
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    Re: Coupled differential equations

    Many thanks... Seems obvious now!
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  4. #4
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    Re: Coupled differential equations

    You will need to do something similar to get a DE for y as well.
    Thanks from MarkFL
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  5. #5
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    Re: Coupled differential equations

    Still working on this...

    I am now trying to understand why the eigenvalues of the matrix of coeff on the RHS are the powers for the solution to the auxilliary equation?
    Can anyone help?
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