M427K Inclass Work8heet 1 Uhlenbeck

Names of students (you may work with your neighbor!)

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The sketch below is of the direction field for an ordinary differential equation. Circle the letter of the equation you think fits.

b) y' = x+1 e) y' = .5xy-3

c) y' = y-2 f) y' = xy - y

An important feature of differential equations is to decide what happens to the solutions of the equation as the independent variable x goes to infinity. Which statement best describes this in the picture?

a) The dependent variable y goes to infinity as x goes to infinity.

b) The dependent variable y goes to zero as x goes to infinity.

c) The dependent variable y goes to 3 1/3 as x goes to infinity.

d) The dependent variable y does not appear to have a limit as x goes to infinity.