Question

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

Answer 1

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.