
#1
Mar1612, 08:16 PM

P: 5

I have the following ODE system
[itex] \begin{cases} x' = v \\ v' = v  \frac{v^3}{3}  x \\ x(0) = x_0 \\ v(0) = 0 \end{cases} [/itex] I am asked to find [itex]x_0>0[/itex] such that the solution [itex](x(t),v(t))[/itex] is periodic. Also, I need to find the period [itex]T[/itex] of such solution. I don't know how to solve the system in the first place (or if it is even possible), so is there a way to figure out what [itex]x_0>0[/itex] will give a periodic solution without solving the system? Thanks! 


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