Phase Portraits of a system of differential equations

[AHSAN MUJTABA]

One thing that bothers me regarding the phase portraits, if I plot a phase portrait, then all my possible solutions (for different initial conditions) are included in the diagram?
In other words, a phase portrait of a system of ODE's is its characteristic diagram?

 

[wrobel]

Yes, the phase portrait gives a complete information about all trajectories. That is why it is so hard to obtain it.