adriank20047 adriank20047

21-01-2024
Mathematics

Answered

For each of the following ODE’s, identify whether or not it is autonomous. Then,
• If it is autonomous, sketch (by hand) a phase line for the equation, making sure to include any fixed points
as well as the ‘arrows’ in between them. (If there are infinitely many fixed points, include a representative
sample of them in your sketch.) Classify each fixed point as stable, unstable, or semi-stable.
• If it is not autonomous, explain why not.

1. x' + 5t = 3x

2. arctan(y) - dy/dx = 0

3. du/dt = u^2 + 2u + 1

Answer :

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