does anyone know anything about slope fields?

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does anyone know anything about slope fields?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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what do you mean by slope fields?
i wanted to know how do we match up the graph of a slope with their differential equation? example if given something like y'= 1+y^2
so u want to know how to solve this

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i think so the problem is that they gave me a bunch of slope fields which is impossible for me to draw online but if you can give me how i should match it up with the graph that would be great
i think u need to solve the DE first and then graph the functions....

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