Determine whether P = e-t is a solution to the d.e.
When P = e-t, the left-hand side of the d.e. is
The right-hand side of the d.e. is
P(1 - P) = P - P2,
which is not equal to -P. Since the left- and right- hand sides of the d.e. are not equal, P = e-t is not a solution to the differential equation.