\begin{equation*} a_n(x)y^{(n)} + a_{n-1}(x)y^{(n-1)} + \cdots + a_2(x)y'' + a_1(x)y' + a_0(x)y = f(x)\text{.} \end{equation*}

\begin{equation*} a_1(x)y' + a_0(x)y = f(x)\text{,} \end{equation*}

\begin{equation*} y' + \us{P(x)}{\ub{\frac{a_0(x)}{a_1(x)}}}y = \us{Q(x)}{\ub{\frac{f(x)}{a_1(x)}}}\text{.} \end{equation*}

\begin{equation*} y' + P(x)y = Q(x) \text{,} \end{equation*}

\begin{align*} \frac{d\mu}{dx} =\amp\ 2\mu \\ \frac{1}{\mu}d\mu =\amp\ 2 dx \\ \int \frac{1}{\mu}d\mu =\amp\ \int 2 dx \\ \ln|\mu| =\amp\ 2x + c \quad (c = 0)\\ \mu =\amp\ e^{2x} \end{align*}