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\title{Ασκήσεις}
\author{ma12449}
\date{}
\begin{document}
\maketitle
\section*{Άσκηση 1 - Διαφορικές Εξισώσεις}
$$
\mu(x)=e^{\int \tan x \, dx}=\frac{1}{\cos x} \notag
$$
Πολλαπλασιάζουμε:
$$
\frac{d}{dx} \left(\frac{y}{\cos x} \right)=\tan x
\Rightarrow \frac{y}{\cos x}=\int \tan x \, dx = -\ln|\cos x|+c
$$
\begin{equation}
 \frac{x^2}{(x+1)^3}= \frac{A}{x+1}+\cdots+\frac{C}{(x+1)^3}
\label{eq:1}
\end{equation}
Με βάση την εξίσωση~\ref{eq:1}
\begin{equation}
       \begin{cases}
             A=1 \\
             2A+B=0 \Rightarrow 2+B=0 \Rightarrow B=2 \\
             A+B+C=0 \Rightarrow 1-2+C=0 \Rightarrow C=1
       \end{cases}
\end{equation}
\begin{align}
       A(x+1)^2 &= A(x^2 +2x +1) = Ax^2+2Ax+A \\
       B(x+1) &= B+B \\
       \Rightarrow x^2 &= Ax^2 + (2A +B) x + (A +B +C) \notag
\end{align}
$$
\lim_{x \to 0} \frac{e^x - \cos x -x \sin x -1}{x^4}
$$
$$
\int_{a=1}^{n}
$$
\end{document}