Assignment 1

due Jan. 18, 2002

 

Note: An entry such as "2.1.6" means question 6 in section 2.1 of Boyce and DiPrima. For plotting, you will find the Direction Field Plotter and Function and Derivative Plotter applets useful.

1.1.3 Solution

1.1.12 Solution

1.1.23 Solution

2.1.5 Solution

2.1.18 Solution

2.1.23 Solution

2.1.26 Solution

E.1. (a)        Plot the direction field for the differential equation y' = y - x/2 on the rectangle $-4 \le x \le 4$, $-3 \le y \le 3$. On the plot, sketch by hand the solution curve that passes through the origin. What happens to y as $x \to \infty$ and as $x \to -\infty$?

(b) What do the isoclines for this differential equation look like? Find an isocline y' = c that is also a solution curve. Hint: what should be the slope of the isocline?

(c) For what initial conditions y(x₀) = y₀ does the solution have the property $y \to +\infty$ as $x \to \infty$?

Solution

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