Activity 7.1.4

Consider the differential equation $$\begin{gathered} \frac{dv}{dt} = 1.5 - 0.5v \end{gathered}$$. Determine, with justification, whether or not each of the following functions is a solution to the differential equation.

1. $v(t) = 1.5t - 0.25t^2$.

2. $v(t) = 3 + 2e^{-0.5t}$.

3. $v(t) = 3$.

4. $v(t) = 3 + Ce^{-0.5t}$ where $C$ is any constant.