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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.$$y^{\prime}=x+y^{2}, \quad(0,0)$$

## Sketch the direction field of the differential equation $y^{\prime}=x+y^{2}$And we have to sketch the solution curve passing through $(0,0)$Direction field and solution curves are shown below.

#### Topics

Differential Equations

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### Video Transcript

pretty of the differential equation. I asked autograph White What? What organ place? What? Once we're of that people once for your But he you can think of these horizontal for apple Waas Why? On the exact facing the bomb which had excellent zero you have the old ones on this tragedy help so negative side That's what most of it so in particular Si is equal to zero watch for no So one no credible have no Hey, take a seat. One wise very plus one one euro one. You know one You go one no long and one grab my life What can you see? See, It's a larger so you get these shells of crab was slumped still always nearly vertical. Now you say between 01 we'll get a problem here are warm in between Yes, you see is going to be less slow before me Let's zero where I will Hey, seems you so the game will have serious problems Yes, it was See that you get a burger towards making ability on the X axis. So field here nearly vory on that axis. So this is the representation of field. So he said Sure nested parabolas. Very, very more more point 00 organs Here. You see that me? Positive fallen function increases sports affinity. That's financial and all that you. So along the x axis he had X people zero. Why are people too wants weird? Why was that for better? That why I had to? Happy that we're so medley that steeper slope gets essentially what we have. I love it as X approaches. Why? Why habits us? No, we have a point. Your hero solution. Okay, zero. Why? Simply Well, So we have that these crime cold 30 year way with these essentially smooth functioning pushed upwards and then began pushed down Today this is one direction. No, I heard that the impossible is go down. Look zero and get her side Exactly.

Ohio State University

#### Topics

Differential Equations

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