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ccurately sketch a phase portrait

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Classify the fixed point at the origin and accurately sketch a phase portrait for each of the following systems

(i) dx/dt=x-2y dy/dt=3x-4y
(ii) dx/dt=3x+2y dy/dt=-2x-2y
(iii) dx/dt=-x-5y dy/dt=x+3y
(iv) dx/dt=x+y dy/dt=-2x-y
(v) dx/dt=2x dy/dt=-x
(vi) dx/dt=2x+2y dy/dt=3x+4y
(vii) dx/dt=x+2y dy/dt=9x+4y
(viii) dx/dt=2x+y dy/dt=-2x+5y

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Solution Summary

Help is given to classify the fixed point at the origin.