Consider the slope field shown. (a) For the solution that...

Consider the slope field shown. (a) For the solution that satisfies y(0) = 0, sketch the solution curve and estimate the following: y(1) ? and y(-1) ? (b) For the solution that satisfies y(0) = 1, sketch the solution curve and estimate the following: y(0.5) ? and y(-1) ? (c) For the solution that satisfies y(0) = -1, sketch the solution curve and estimate the following: y(1) ? and y(-1) ?

Transcript

00:01 Hi, in this question, we're going to use this slope field that's shown and try to graph some solutions.

00:11 So let me first try to just, let me do this in black.

00:20 First i'll just draw these axes.

00:27 And then we have one, two, one, two.

00:38 So first for a, i'll do a in red, it passes through y of zero equals zero.

00:46 So what we do is we start at this point, and then we just try to follow the slope of, we just try to follow the slope of the lines, and we sort of draw a graph.

00:57 So it starts off looking pretty horizontal, but gradually goes up like this, and kind of goes more up and up as we go here.

01:08 And then on the other side, it also starts a little horizontal, and it's sort of hard to tell exactly what's going on.

01:19 But it looks like it kind of almost is like a straight line like this.

01:26 So something like here.

01:35 So what you might decide for y of 1 and y of negative 1 is sort of arbitrary, but we might say 1 comma 1.

01:46 So we might say this is equal to 1.

01:50 And at negative 1, we might say that we're at, well, let's see a negative 1.

01:58 Maybe we'll say we're at 1 half.

02:01 As long as you get the signs right, i think you'll probably be on the right track.

02:07 But they should both be positive.

02:10 Then we'll do b.

02:11 So now y of 0 is 1.

02:13 So we start at this point here.

02:16 And so we see that on the right, we're already going like, we're already going very up...

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