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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.

Differential Equations

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Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Boston College

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