5.3 - Euler'S Method Equation Worksheet Page 6
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6WS 5.3: Euler’s Method
Calculus Maximus
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
. Use Euler’s method, starting at
x
f
0
1
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
f
or greater than
0.4
. Explain your reasoning.
Page 6 of 6
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