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

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\shade{gray}{Imhomogeneous equation} $y' + ay = b$ with $b$ any function.
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\begin{enumerate}[noitemsep]
    \item Compute $y_p = z(x) e^{-A(x)}$ with $z(x) = \int b(x) e^{A(x)} \dx x$ ($A(x)$ in exp here!),  
    \item Solve and the result is $y(x) = y_h + c \cdot y_p$. For initial value problem, determine coefficient $C$
\end{enumerate}