Given the system of differential equations x &#x2032; </msup> = 2 x +

Hailie Blevins

Hailie Blevins

Answered question

2022-06-22

Given the system of differential equations x = 2 x + y 3 and y = y i found the flow
ϕ t ( x , y ) = ( ( x 0 + 1 / 5 y 0 3 ) e 2 t 1 / 5 y 0 3 e 3 t , y 0 e t )

Answer & Explanation

pheniankang

pheniankang

Beginner2022-06-23Added 22 answers

Since y = y 0 e t , there are no periodic solutions. If a solution had period T > 0, then y 0 ( t + T ) = y 0 e t , clearly impossible unless y 0 = 0. If y 0 = 0, x = x 0 e 2 t and a similar argument applies.

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