Solving Differential Equations

1. [3 points] y' = 2/3y − 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' = −y^2 + 10y − 21    y(0) = 1 y(0) = 4

4. [5 points] y' = 9y − y^3     y(0) = −4 y(0) = −1 y(0) = 2 y(0) = 4

you have 2 hours to finish

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