Euler'S Method Worksheet With Answers Page 6
ADVERTISEMENT
1
2
3
4
5
6Calculus Maximus
WS 5.3: Euler’s Method
10. AP 2005-4 (No Calculator)
dy
Consider the differential equation
2
x y
.
dx
(a) On the axes provided, sketch a slope field for the given differential equation at the twelve points
indicated and sketch the solution curve that passes through the point 0,1 .
3
(b) The solution curve that passes through the point 0,1 has a local minimum at
x
ln
. What is
2
the y-coordinate of this local minimum?
(c) Let y
f x be the particular solution to the given differential equation with the initial condition
f
0
1
. Use Euler’s method, starting at
x
0
with two steps of equal size, to approximate
f
0.4
. Show the work that leads to your answer.
2
d y
(d) Find
in terms of x and y. Determine whether the approximation found in part (c) is less than
2
dx
or greater than
f
0.4
. Explain your reasoning.
Page 6 of 6
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education