Coupled Equations. In analyzing coupled equations of the form
where
are constants, we may wish to determine the relationship between x and y rather than the individual solutions x(t), y (t) For this purpose, divide the first equation by the second to obtain
This new equation is homogeneous, so we can solve it via the substitution v = y/x. We refer to the solutions of (17) as integral curves. Determine the integral curves for the system
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