Mathematics 134 – Intensive Calculus for Science 2 Discussion 4 – Slope Fields April 4, 2006

Group:

Discussion Questions

A) The plot shows the slope field for \frac{dy}{dx} = x(y − 1)

1) Sketch the solutions passing through the points (0, −1), (0, 1), (0, 2) (you should get three different graphs).

2) From your sketch, write down the equation of the solution with y(0) = 1.

3) Check your solution to part 2 by substituting it into the differential equation.

B) This plot shows the slope field for \frac{dy}{dx} = x + y

1) Sketch the solutions passing through the points (−1, 0), (−3, 1), (0, 0) (you should get three different graphs again).

2) From your sketch, guess the equation of the solution with y(−1) = 0.

3) Check your solution to part 2 by substituting it into the differential equation.

Assignment

Group writeups due Wednesday, April 5.