Please help with the attached problem, thank you! 7. Provide time-series sketches \((x \text{ vs } t \text{ and } y \text{ vs } t)\) for each of the solution curves depicted in the following phase planes.**Diagram Descriptions:****(a)** - **Illustration:** The phase plane shows a circular solution curve centered around the origin. The arrows indicate a counterclockwise rotation around the origin.- **Initial Condition (I.C.):** There is a marked point on the positive y-axis.- **Explanation:** This represents a stable limit cycle with trajectories rotating in a circular manner.**(b)**- **Illustration:** The phase plane displays a spiral-inward pattern originating from a point and spiraling towards the origin.- **Initial Condition (I.C.):** The starting point is slightly redirected clockwise from the positive y-axis.- **Explanation:** This suggests a spiral sink where trajectories spiral inwards to the origin.**(c)**- **Illustration:** The phase plane graph has arrows pointing outward, away from the origin in each direction.- **Initial Condition (I.C.):** The marked point is in the first quadrant, creating a radial line.- **Explanation:** This indicates an unstable node where trajectories move directly away from the origin.**(d)**- **Illustration:** The phase plane features an arrowed path curving from the marked point towards the origin.- **Initial Condition (I.C.):** The point is in the fourth quadrant, indicating an inward trajectory.- **Explanation:** This shows a saddle point behavior, where trajectories come towards and then pass by the origin.Each time-series sketch should reflect the specific dynamics of the corresponding phase plane trajectories as described above.

Name: Please help with the attached problem, thank you! 7. Provide time-seri
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please help with the attached problem, thank you! 7. Provide time-series sketches \((x \text{ vs } t \text{ and } y \text{ vs } t)\) for each of the solution curves depicted in the following phase planes.**Diagram Descriptions:****(a)** - **Illustrat

a. The functions are x=4cost and y=4sint x=4cost: ; y=4sint: c. The functions are x=3t and y=3t x=3t: ; y=3t: Note: Post the remaining phase plane separately.