Question

Consider the following slope fields. (a) 3 (b) 3 (c) 3 2 2 2 1 1 1 0 0 0 -1 -1 -1 -2 -2 -2 -3 -3 -3 3 -2 -1 0 1 2 3 x 3 -2 -1 0 1 2 3 x 3 -2 -1 0 1 2 3 x i) Match each of the slope fields above to the corresponding differential equation below. Write the letter A, B, or C in each of the blank spaces to indicate the corresponding slope field. $\frac{dy}{dx} = (y^2 - 4)(y - 1)$ ___ $\frac{dy}{dx} = (x^2 - 4)(x - 1)$ _ $\frac{dy}{dx} = cos x$ ___ ii) On each slope field above, sketch the solution curve that satisfies the initial condition $y(1) = \frac{3}{2}$ Note: Make sure you draw your solution curves to extend as far as possible in both directions.

          Consider the following slope fields.
(a) 3
(b) 3
(c) 3
2
2
2
1
1
1
0
0
0
-1
-1
-1
-2
-2
-2
-3
-3
-3
3 -2 -1 0 1 2 3
x
3 -2 -1 0 1 2 3
x
3 -2 -1 0 1 2 3
x
i) Match each of the slope fields above to the corresponding differential equation below. Write the letter A, B, or
C in each of the blank spaces to indicate the corresponding slope field.
$\frac{dy}{dx} = (y^2 - 4)(y - 1)$ _____
$\frac{dy}{dx} = (x^2 - 4)(x - 1)$ _____
$\frac{dy}{dx} = cos x$ _____
ii) On each slope field above, sketch the solution curve that satisfies the initial condition
$y(1) = \frac{3}{2}$
Note: Make sure you draw your solution curves to extend as far as possible in both directions.

Consider the following slope fields.
(a) 3
(b) 3
(c) 3
2
2
2
1
1
1
0
0
0
-1
-1
-1
-2
-2
-2
-3
-3
-3
3 -2 -1 0 1 2 3
x
3 -2 -1 0 1 2 3
x
3 -2 -1 0 1 2 3
x
i) Match each of the slope fields above to the corresponding differential equation below. Write the letter A, B, or
C in each of the blank spaces to indicate the corresponding slope field.
(dy)/(dx) = (y^2 - 4)(y - 1)
(dy)/(dx) = (x^2 - 4)(x - 1)
(dy)/(dx) = cos x
ii) On each slope field above, sketch the solution curve that satisfies the initial condition
y(1) = (3)/(2)
Note: Make sure you draw your solution curves to extend as far as possible in both directions.

Added by Bridget G.

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