Question

When a differential equation has periodic solution

Answer 1

We define a system of differential equations by

dxdtdydt=x+y−x(x2+3y2)=−x+y−2y3.

We want to show that there exists a periodic solution to this problem. The first step is to transform the system into polar coordinates; some calculating gives us:

drdtdθdt=r(1−r2)−r3⋅sin2(θ)=−1r2+tan(θ).

Answer 2

Answer:

here is your answer..........