Answer:
Step-by-step explanation:
a. Create a direction field for the specified differential equation
b. By observing the direction field, comment on the behavior of the solutions as t becomes large.
The solutions seem to oscillate
All solutions appear to approach the function y0(t)=4
All solutions seem to converge to the function y0(t)=0
All solutions appear to have negative slopes eventually and thus decrease indefinitely
All solutions seem to have positive slopes eventually and therefore increase without limit
C
As t approaches infinity
All solutions seem to exhibit positive slopes eventually and thus decrease indefinitely
The solutions seem to gradually approach the function y0(t)=0
All solutions appear to eventually have negative slopes leading to decrease without bounds
All solutions seem to converge to the function y0(t)=4
The results are oscillatory
This equation can be solved with two solutions, corresponding to
and
.
The solution is 57 because I excel at mathematics; it's my forte.
