Explain why the functions with the given graphs can't be solutions of the differential equation dy dt = et(y − 1)2.

Please see attached document for the graphs:

The functions with the given graphs can't be solutions of the differential equation dy dt = et(y − 1)2.

(a) won’t work, since it has negative slope on portions of its solutions. The slope, e t (y − 1)2 , is a nonnegative function.

(b) won’t work, since it has positive slope at y = 1, where the slope must be flat.

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