\newsectionNoPB
\subsection{Linear differential equations of first order}
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\shortproposition Solution of $y' + ay = 0$ is of form $f(x) = z e^{-A(x)}$ with $A$ anti-derivative of $a$

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\shade{gray}{Imhomogeneous equation} 
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\begin{enumerate}[noitemsep]
    \item Plug all values into $y_p = \int b(x) e^{A(x)}$ ($A(x)$ in the exponent instead of $-A(x)$ as in the homogeneous solution)
    \item Solve and the final $y(x) = y_h + y_p$. For initial value problem, determine coefficient $z$
\end{enumerate}