@dharr  @Rouben Rostamian  it is first time i face this How we can calculate this even by hand if lecture exist  please mention it? if we can do phase portrait of system by Conserved quantity so we don't need the jacobian even?  always is times by -1/2?

@Rouben Rostamian  thank you so much , it seems you are a profisional in this topic i am glad to have you here.

@Rouben Rostamian   i didn't know which we can do that by maple, really is so good, i saw a lot of phase portrait with a lot of design is been a while i am searching for finding and plot them this is good really, but the direction of trajectory is missing can we have the direction and point inside the plot are shown?

i saw a lot of phase portrait this is so good and i am looking for this code, and other code too for my work

@janhardo thank you so much 

@Rouben Rostamian  i have two question! one is personal :  regarding to your name are you persian?
secondly: how you give the initial condition to system is arbitrary?

@Rouben Rostamian  thank you so much, i will ask more question about this topic