Let us consider the equation
\begin{equation}
\frac{dx}{dt} = x^2 - 4x + \lambda\tag{1.7.3}
\end{equation}
as a family of differential equations indexed by the parameter \(\lambda\text{.}\) If we let \(f_\lambda(x) = x^2 - 4x + \lambda\text{,}\) then
\begin{equation*}
\frac{dx}{dt} = f_\lambda(x)
\end{equation*}
is a called one-parameter family of differential equations. For each value of \(\lambda\text{,}\) we obtain an autonomous differential equation, and for each value of \(\lambda\text{,}\) we have a different phase line to examine.