Question

Consider the following differential equation. (A computer algebra system is recommended.) (1 + t2)y' + 4ty = (1 + t2)−2 (a) Draw a direction field for the given differential equation.

Answer 1

Answer:

Step-by-step explanation:

a. Draw a direction field for the given differential equation

b. Based on the inspection of the direction field, describe ow solutions behave for large t.

The solution appear oscillatory

All solutions seems to converge to the function y0(t)=4

All solutions seems to converge to the function y0(t)=0

All solutions seems to seems to eventually have negative slopes a and hence decrease without bound

All solutions seems to seems to eventually have positive slopes a and hence increase without bound

C

As t-infinity

All solutions seems to seems to eventually have positive slopes a and hence decrease without bound

All solutions seems to converge to the function y0(t)=0

All solutions seems to seems to eventually have negative slopes a and hence decrease without bound

All solutions seems to converge to the function y0(t)=4

The solution are oscillatory