Solving Differential Equations

Homework Section 10.5

MTH 122

Name: ________________________________________

Directions:

Complete all questions. Your work must be legible, neat, and complete. Show your work and provide explanations where needed. All pages need to be stapled. All graphs need to be drawn neatly and any lines should be drawn using a straight edge.

Questions:

One or more initial conditions are given for each differential equation. Use the qualitative theory of autonomous differential equations to sketch the graphs of the corresponding solutions. Include a yz-graph. Always indicate the constant solutions on the ty-graph whether they are mentioned or not.

1. [3 points] y′ = 23 y − 3 y(0) = 3 y(0) = 6

2. [4 points] y′ = (y − 1)(y − 5) y(0) = −2 y(0) = 2 y(0) = 4 y(0) = 6

3. [3 points] y′ = −y2 + 10y − 21 y(0) = 1 y(0) = 4

4. [5 points] y′ = 9y − y3 y(0) = −4 y(0) = −1 y(0) = 2 y(0) = 4