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Homework Help: Partially Decoupled System?

  1. Oct 29, 2013 #1
    The problem statement, all variables and given/known data

    dx/dt = 2x - 3y2
    dy/dt = -3y

    Derive the general solution and find the solution that satisfies the initial values: x(0) = 0 and y(0) = 1.

    The attempt at a solution

    dy/dt = -3y
    y(t) = c1e-3t

    dx/dt = 2x - 3(c1e-3t)2

    I have no idea where to go from here. Any help?
  2. jcsd
  3. Oct 29, 2013 #2


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    Science Advisor
    Gold Member

    The equation ##\frac{dx}{dt}-2x=-3(c_{1}e^{-3t})^{2}## is just a linear, inhomogenous 1st order DE. The method of solving it is multiplying both sides of the eq with the integrating factor ##e^{-2t}## and using the "derivative of product" rule to get ##\frac{d}{dt}(e^{-2t}x)=-3e^{-2t}(c_{1}e^{-3t})^{2}##. This equation can be directly integrated to find the function x(t).
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