Skip to main content\(\newcommand{\dollar}{\$}
\DeclareMathOperator{\erf}{erf}
\DeclareMathOperator{\arctanh}{arctanh}
\DeclareMathOperator{\arcsec}{arcsec}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Activity 7.1.4.
Consider the differential equation
\begin{equation*}
\frac{dv}{dt} = 1.5 - 0.5v\text{.}
\end{equation*}
Determine, with justification, whether or not each of the following functions is a solution to the differential equation.
(a)
\(v(t) = 1.5t - 0.25t^2\text{.}\)
(b)
\(v(t) = 3 + 2e^{-0.5t}\text{.}\)
(c)
(d)
\(v(t) = 3 + Ce^{-0.5t}\) where
\(C\) is any constant.
