Euler's Method
Slope Fields
Logistic
Separables
100
The change in x used in the table method (usually given).
step size
100
A graphical representation of the solutions of a first-order differential equation
slope field
100
The condition of a system usually represented by the variable "L".
carrying capacity
100
Is y' = x - xy separable?
Yes
200
Used to approximate the actual solution curve
sets of linearizations
200
What is the slope of y'= y + xy + 20.1x at the point (2,1)?
43.2
200
The value represented by the inflection point on a logistic curve.
half the carrying capacity
200
What is the general solution to y' = 2y + 1?
y = Ce^2x − 1/2
300
Use Euler's Method with a step size of 0.2 to estimate y(1.2), where y(x) is the solution to the initial value problem y'=y-2x, with y(1)=0
y=-0.4
300
The curve plotted through a slope field given an initial condition (in the form of a point).
solution curve
300
The rate of growth is increasing on this interval.
zero to the inflection point (Also accept first half of curve)
300
Find the solution to the differential equation y' = 2 - y given the initial condition y(0) = 0.
y = 2(1 − e^(−x))
400
Use Euler's Method with a step size of 0.1 to estimate y(0.2), where y(x) is the solution to the initial value problem y'=-(x/y), with y(0)=1
y=.99
400
http://s3.amazonaws.com/answer-board-image/2009429156126337661437212500007200.jpg
1-d 2-c 3-b 4-a
400
The interval in which the rate of growth is decreasing.
the inflection point to infinity (Also accept second half of the curve)
400
In a population of fixed size S, the rate of change of the number N of persons who have heard a rumor is proportional to the number of those who have not yet heard it. Model this situation with a differential equation.
N' = k(S − N)
500
Use Euler's Method to estimate y(1) using a step size of 0.1, if y'=x+(y/5)
y(1) ≈ -3.182
500
What is the initial condition of this solution curve? http://ww2.math.buffalo.edu/306/py/306ch1_slope_field_soln_1.3.5.png
(-4,3.5)
500
The general solution to a logistic differential equation.
1/(1+Ae^(-kt))
500
Find the general solution to dy + 7x(dx) = 0
y=−​3.5x^2 + C
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