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Worksheet Key Terms & Concepts
β³οΈ First-Order Differential Equations.
First-Order Differential Equation
Every first-order differential equation can be written in the form
\begin{equation*}
f(x, y, y') = 0\text{.}
\end{equation*}
This just means that all the terms in the equation have been moved to the left-hand side, which can only contain the independent variable, \(x\text{,}\) the dependent variable, \(y\text{,}\) and its derivative, \(y'\text{.}\)
β³οΈ Separation of Variables.
First-Order Separable Differential Equation
These equations can be written as:
\begin{equation*}
\frac{dy}{dx} = f(x) \cdot g(y).
\end{equation*}
Separation of Variables Method
A solution technique for separable equations. It involves isolating
\(y\) and
\(x\) terms on opposite sides, followed by integration.
