Chapter 2.1, Problem 36P

In Problems $29$ through $36$, obtain the requested results by solving the given equations analytically or, if necessary, by graphing numerically generated approximations to the solutions.

Consider the initial value problem $y\text{'}=ty(4-y)/(1+t),y\left(0\right)=y_0>0$

Determine how the solution behaves as $t\to \infty$.

If $y_0=2$, find the time $T$ at which the solution first reaches the value $3.99$.

Find the range of initial values for which the solution lies in the interval $3.99<y<4.01$ by the time $t=2$.