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.
 

Thread 'A question about variables of integration'

I have the equation ##F^x=m\frac {d}{dt}(\gamma v^x)##, where ##\gamma## is the Lorentz factor, and ##x## is a superscript, not an exponent. In my textbook the solution is given as ##\frac {F^x}{m}t=\frac {v^x}{\sqrt {1-v^{x^2}/c^2}}##. What bothers me is, when I separate the variables I get ##\frac {F^x}{m}dt=d(\gamma v^x)##. Can I simply consider ##d(\gamma v^x)## the variable of integration without any further considerations? Can I simply make the substitution ##\gamma v^x = u## and then...
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