Use the method discussed under “Homogeneous Equations” to solve problems 9-16.
Homogeneous equation for the given equation is .
If the right-hand side of the equation can be expressed as a function of the ratio alone, then we say the equation is homogeneous.
Let us take .
Now, integrate on both sides.
Let us take . Then,
Therefore, Homogeneous equation for the given equation is .
Question: Coupled Equations. In analyzing coupled equations of the form
where a, b, 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 . We refer to the solutions of (17) as integral curves. Determine the integral curves for the system
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