Consider the set of equations: [y' = z; |z'+z= ln (1-3y+y-z). 1. Find the fixed point...

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Consider the set of equations: [y' = z; |z'+z= ln (1-3y+y²-z). 1. Find the fixed point of this system and then linearise the set around the fixed point. 2. Determine the character of the fixed point. Plot qualitatively a phase portrait of the system in the vicinity of each fixed point. Consider the set of equations: [y' = z; |z'+z= ln (1-3y+y²-z). 1. Find the fixed point of this system and then linearise the set around the fixed point. 2. Determine the character of the fixed point. Plot qualitatively a phase portrait of the system in the vicinity of each fixed point.