NAME:
UBC ID:
LAB GROUP:
MECH 221 Computer Lab 4: Prelab Worksheet
Consider the following ODE, for which a slope field is shown below:
dy
3x2 + 2x
=
.
dx
3y 2 − 1
(∗)
Slope field for (3y2−1)y’ = 3x2 + 2x
2
1.5
1
y
0.5
0
−0.5
−1
−1.5
−2
−2
−1.5
−1
−0.5
0
x
0.5
1
1.5
2
Print a copy of this sheet, two-sided if possible, and complete the activities on the back. Show your
work in the spaces provided. Do the work by hand, not by computer. Make a copy for your own
use during the lab: you may need it after the original has been handed in.
Important: Activities 1–4 can be completed without solving the given differential equation. Solving (∗) prematurely would be a waste of effort that could actually make these questions harder
than they need to be!
File “prelab4”, version of 23 October 2014, page 1.
Typeset at 13:43 October 23, 2014.
2
MECH 221 Computer Lab 4: Prelab Worksheet
1. Find an equation or equations for the set of (x, y) points where dy/dx is undefined. Show and label
those points on the sketch provided.
2. Find an equation or equations for the set of (x, y) points where dy/dx = 0. Show and label those
points on the sketch provided.
3. Find an equation for the set of (x, y) points where dy/dx = 1. Those points lie on a certain conic
section: give the standard name for this shape. Show and label those points on the sketch provided.
4. Find an equation for the set of (x, y) points where dy/dx = −1. Those points lie on a certain conic
section: give the standard name for this shape. Show and label those points on the sketch provided.
5. Solve ODE (∗). Produce a formula for the function g(x, y) such that g(0, 0) = 0 and every solution
curve for (∗) satisfies g(x, y) = C for some constant C.
Then, identify the value of C associated
with the solution curve passing through (x, y) = 0, 53 .
File “prelab4”, version of 23 October 2014, page 2.
Typeset at 13:43 October 23, 2014.