Chapter 9.3, Problem 54E

a.

To determine

The general solution of the equation $y{y}^{\prime }\left(t\right)=\frac{1}{2}{e}^t+t$ and express it explicitly as a form of t for $y>0\text{ and }y<0$.

b.

To determine

The solution of the equation $y{y}^{\prime }\left(t\right)=\frac{1}{2}{e}^t+t$ that satisfy the initial conditions $y\left(-1\right)=1$ and $y\left(-1\right)=2$.

c.

To determine

To describe: The behavior of the solution of the part (b) as t increases.

d.

To determine

To find: The solution of the differential equation that satisfy the initial conditions $y\left(-1\right)=-1$ and $y\left(-1\right)=-2$.

e.

To determine

To describe: The behavior of the solution of the part (b) as t increases.