[Analysis] Setup and start

semester3/analysis-ii/parts/diffeq/00_intro.tex

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+\subsection{Introduction}
+\shortex $f'(x) = f(x)$ has only solution $f(x) = ae^x$ for any $a \in \R$;
+$f' - a = 0$ has only solution $f(x) = \int_{x_0}^{x} a(t) \smallhspace \dx t$
+
+\setcounter{all}{6}
+\shorttheorem Let $F: \R^2 \rightarrow \R$ be a differential function of two variables. Let $x_0 \in \R$ and $y_0 \in \R^2$.
+The Ordinary Differential Equation (ODE) $y' = F(x, y)$ has a unique solution $f$ defined on a ``largest'' interval $I$ that contains $x_0$ such that $y_0 = f(x_0)$