Unit 08 Core Practice

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Core pathway

Differential Equations & Numerical Models

College-level fluency, interpretation, and verification.

1. For y′=y(2−y), identify equilibria.

2. Which statement best describes the central reasoning in Direction Fields, Equilibria & Qualitative Behavior?

3. Use one Euler step with h=0.1 for y′=x+y, y(0)=1.

4. Which statement best describes the central reasoning in Euler’s Method & Global Error?

5. Solve y′=xy, y(0)=3.

6. Which statement best describes the central reasoning in Separable Differential Equations?

7. A population doubles in 6 years. Find k.

8. Which statement best describes the central reasoning in Exponential Growth, Decay & Half-Life?

9. For P′=.2P(1−P/1000), when is growth fastest?

10. Which statement best describes the central reasoning in Logistic Growth & Carrying Capacity?

11. Solve y′+y=e^x.

12. Which statement best describes the central reasoning in First-Order Linear Equations & Integrating Factors?

β Beta Program