Question: Please help. Need it done by 3 hours Consider the following first-order ODEs: dx = x 1+ dt 1+ x2 dx =-rx+ dt 1+ x

Please help. Need it done by 3 hours

Consider the following first-order ODEs: dx = x 1+ dt 1+ x2 dx =-rx+ dt 1+ x a) Find all the fixed points. b) Find any critical values r at which bifurcations occur. What type of bifurcations occur (saddle-node, transcritical, supercritical pitchfork, or subcritical pitchfork)? c) Classify the stability of the fixed points. Collect your results in a table. d) Sketch the bifurcation diagram: x* versus r. e) Sketch the phase portraits and corresponding solutions for each qualitatively different behavior

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