Register to reply 
Find initial condition such that ODE solution is periodic 
Share this thread: 
#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! 


Register to reply 
Related Discussions  
?Find an initial velocity v such that theres no oscillation,is my solution correct  Introductory Physics Homework  38  
Find solution with initial value  Differential Equations  7  
Find a particular solution that satisfies the intial condition  Calculus & Beyond Homework  1  
Initial condition leads to periodic solution  Differential Equations  2  
Initial values lead to periodic solution  Calculus & Beyond Homework  5 