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8 lines
492 B
TeX
8 lines
492 B
TeX
\subsection{Introduction}
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\shortex $f'(x) = f(x)$ has only solution $f(x) = ae^x$ for any $a \in \R$;
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$f' - a = 0$ has only solution $f(x) = \int_{x_0}^{x} a(t) \smallhspace \dx t$
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\setcounter{all}{6}
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\shorttheorem Let $F: \R^2 \rightarrow \R$ be a differential function of two variables. Let $x_0 \in \R$ and $y_0 \in \R^2$.
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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 $y_0 = f(x_0)$
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