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\begin{document}

\begin{center}
  \Large{8. Gyak.}  

  Szétválaszthatóra visszavezethető egyenletek
  \end{center}

\medskip

\begin{enumerate}
 \item \underline{Homogén $y'=f\left(\frac{y}{x}\right)$}
 \begin{enumerate}
   \item $(5x-7y)-(x+y)y'=0, \ y(1)=1$
   \item $x y'=x \sin\left(\frac{y}{x}\right)+y, \ y\left(\frac12\right)=\frac{\pi}{4}$
   \item $y'=\frac{y^2-x^2}{x y}$
   \item $3x y^2 y'=x^3+3y^3, \ y(2)=1$
 \end{enumerate}
 \item \underline{$y'=f(a x+b y+c)$}
 \begin{enumerate}
   \item $y'=-\frac52 +\sin(5x+2y)$
   \item $y'=\tan(y-x)+1$
   \item $y'=\sqrt{x+2y+1}+2x+4y+2$
   \item $y'=\frac{1}{3x-2y+2}$
   \item $y'=e^{2y-6x+1}+3, \ y(0)=0$
   \item $y'=4+\cos(-5x+2y+3), \ y(1)=1$
 \end{enumerate}
 \item \underline{$y'=f\left(\frac{a x+b y+c}{\alpha x+\beta y+\gamma}\right)$}
 \begin{enumerate}
   \item $y'=\frac{7x-5y+45}{9x+21y+3}$
   \item $y'=\frac{x+y-1}{2x+2y-1}$
   \item $(x+y)^2 y'=(x+y+2)^2$
 \end{enumerate}
\end{enumerate}

\begin{figure}[ht]
\centering
\includegraphics[width=0.55\textwidth]{integral}
\caption{$y'=4+\cos(-5x+2y+3)$}
\end{figure}

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