Question

On a print-out of these slope fields, sketch for each three solution curves to the differential equations that generated them. Then complete the following statements: For the slope field in figure 1. a solution passing through the point (0.-1) has slope. For the slope field in figure 1. a solution passing through the point (-2.2) has slope. For the slope field in figure 2. a solution passing through the point (1.-3) has slope For the slope field in figure 2. a solution passing through the point (0.4) has a slope.

Answer 1

The slopes of the figures 1 , 2 & 3 are 0 , 1 & 1/3 respectively.

Given, two figures with the lines passing through different points

we have to find the slopes of different figures.

Now, in figure 1 curve passes through (0 , -1)

as, 2x + 2yy' = 0

y' = -x/y

y' = -(0)/-1

y' = 0

Now, in figure 2 curve passes through (-2 , 2)

as, y ' = -x/y

y' = -(-2)/2

y' = 1

In figure 3 curve passes through (1 , -3)

as, y' = -x/y

y' = -1/-3

y' = 1/3

So, the slopes of the figures 1 , 2 & 3 are

0 , 1 & 1/3 respectively.

Hence, the slopes of the figures 1 , 2 & 3 are 0 , 1 & 1/3 respectively.

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