Question

Can anyone help me with this?

A model of seasonal growth is given by
dx/dt=rx cos(wt)
where r and w are constants. Illustrate the behaviour of the solution x of this equation.

Answer 1

\[\frac{ dx }{ dt } =r*x *\cos(wt)\]
as r and w are constants
then we can apply product rule on the eq

\[\frac{ dx }{ dt } = (r*x) *(\cos(wt))\]
(r*x) = f(x)
cos(wt) = g(x)
\[\frac{ dx }{ dt } = f(x)*g \prime(x) + f \prime(x) *g(x)\]

Answer 2

This is what i got from the equation.\[x=x_0 e ^{\frac{ r }{ w } \sin(wt)}\]But now, how should I explain about the behaviour of this solution?