Chapter 2.2, Problem 8P

In each of Problems 1 through 12:

Draw a direction field for the given differential equation.

Based on an inspection of the direction field, describe how solutions behave for large $t$.

Find the general solution of the given differential equation, and use it to determine how solutions behave as $t\to \infty$.

$(1+t^2)y\text{'}+4ty={(1+t^2)}^{-2}$