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\author{ma13060}
\title{Ασκήσεις}
\begin{document}
\maketitle
\section*{Άσκηση 1 - Διαφορικές Εξισώσεις}
$$
	\mu(x) = e^{\int \tan x\,dx} = \frac{1}{\cos{x}}
$$
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}
\end{equation}
Με βάση την εξίσωση 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 \notag \\
	B(x+1) &= Bx+B \\
	\Rightarrow x^2 &= Ax^2 + (2A+B)x + (A+B+C) \notag 
\end{align}
$$
	\lim_{x \to 0} \frac{e^c - \cos x - x\sin x -1}{x^4}
$$
$$
	\int_{a=2}^{n}
$$
\end{document}
