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12-38.
  1. The diagram below shows a slope field. Homework Help ✎
    diagram at right

    1. Explain why must be a function of both x and y.

    2. Sketch a solution curve that passes through (0, 3).

    3. The slope field is for the differential equation . Find the equation of your solution curve.

Are the slopes in the diagram parallel anywhere?

Your curve should look like a bell-shaped curve with a maximum at (0, 3) and a horizontal asymptote of y = 0.

Once you integrate you should have a '+ C'. Use the point (0, 3) to solve for the value of C.