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# Sketch the direction field of the differential equation. Then use it to sketch a solution curve that passes through the given point.$y' = y + xy, (0,0)$

## $$\begin{array}{|c|c|c|}\hline x & y & y^{\prime}=y+x y \\\hline 0 & \pm 2 & \pm 2 \\1 & \pm 2 & \pm 4 \\-3 & \pm 2 & 74 \\\hline\end{array}$$

#### Topics

Differential Equations

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### Video Transcript

you're giving in the court? Us? I smoke field French. Yeah, a solution. French equation given y prime. That's why Appointment 01 already grab. So feel there is that very given well number scene. Why? Why different conclusions? White crime. Why? Why, girl? That's why such a day we'll see. And so we have one one 90 See one We'll see that it is a translation. Reciprocal function. Why one if x is equal and original baking tells Is that why? Why minus wide zero You have the slope along the winding one for zero dysfunction The x and y Yes, we already determined Wando next equals negative one. We have that white, you know. He also had set c 40 Why is it zero? I want one. So long, Texas. Your whole you. It's easy. Positive one y z one of one plus it's It's simply function white water. Correct one. Have NASA negative one white. The slope of these points will be before one. So we had appointed 01 yes, and point at negative 0.0.5. So one well have a point one more slopes in between along this year He also pointed and made a 1.5 committed to. So do you see that? As seen increases. They're taking reciprocal function, checked over by one, and we are essentially structure every one direction. And so is he stretched for Aaron Berger? Yeah, thanks. It's looks are also getting steeper. So approximation of this fiction. We have more hyperbole. It's burns. Purcell. Get to a point where they're essentially vertical. I didn't see that, you see is somewhere between 01 We have a contraction function. White was one of the 1%. So what had slopes that air in truly 01 in between? That one negative zero her white now see is say negative one. Then why is equal to negative 11? Sex to be ocean white. One of the 1% What woman? Its axis. The point is going to have a slope of negative, particularly zero idea warning. It would 0.5 minutes in the second quarter of seven going on happen one one No. One as it's more than one negative. The paper was further and further away from zero. Yeah, so approximation of this. It's growing. The general idea is as effortless. It literally from that point almost and see the sea of between zero and one. I would have said zero. Yeah, one day. And so we get what looks like it's sort of dining pattern here, for we seem to have Most of the zero slow points are concentrated around the acid toots Sequels named of one light zero. This is our slope. You now to find solution 0.1 First fund went 01 on this graph and his ex purchasing thing on the right. It's well, we're rapidly like next time for function. Grab, purchase. Yeah, Experts, The graph crazy The explosion closing Lying. Why? People zero. We're flatten them again. Sort of like a next.

Ohio State University

#### Topics

Differential Equations

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