A Phase Portraits of a system of differential equations

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

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