1. Clicker Question 1 The DE y y  + x2 y2 = ex is:
A. linear and separable
B. linear but not separable
C. separable but not linear
D. neither separable nor linear

2. Parametric Equations (10/30/13)
Question: How might we describe an infinity symbol analytically?
Note that this curve fails both the vertical and horizontal line tests, so we can’t write y as a function of x nor x as a function of y.
Perhaps we can describe both x and y as functions of a third variable t.
t is called a parameter, and the equations for x and y in terms of t are called parametric equations.

3. Plotting points and eliminating the parameter
For our infinity sign, try the equations x = 2sin(t), y = sin(2t) for 0  t  2 .
Plot some points!
Note that we may be able to use algebra to eliminate t (if we wish), obtaining y as a function of x or the other way around.
Try this with the equations above.

4. A Simpler Example
What do the equations x = t 2 – 2t and y = t + 1 look like?
Plot some points!
Write x as a function of y.

5. Clicker Question 2
If x = sin(t) and y = tan(t), what is y as a function of x?
A. y = arctan(x)
B. y = x / (1 – x 2)
C. y = x / (1 – x 2)
D. y = (1 – x 2)
E. y = tan(sin(x))

6. More Curves What is x = cos(t), y = sin(t), 0  t  2 ?
What is x = t cos(t), y = t sin(t), 0  t  4 ?

7. Clicker Question 3 What is x = sin(t), y = cos(t), 0  t   ?
A. A circle
B. An upper semi-circle
C. A lower semi-circle
D. A right-hand semi-circle
E. A left-hand semi-circle

8. Assignment for Friday Hand-in #2 is due at class time.
Read Section 10.1.
In that section please do Exercises 1-15 odd and 28.