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\begin{center}
  \huge{9. Gyak.}  

  Lineáris inhomogén, Bernoulli
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\begin{enumerate}
 \item Lineáris
 \begin{enumerate}
   \item $y'+\frac{1}{x}y=x^3, \ y(1)=1$
   \item $x y' -y = x^3+1, \ y(1)=2$
   \item $y' -\frac{4}{x}y = x^2+x$
   \item $y'-2y =3 \cdot e^{2x}$
   \item $y'+2 x y =2x \cdot  e^{-x^2}$
   \item $y'-(\tan x) y+ \sin x=0 $
   \item $x y' +2y = 3x, \ y(1)=0$
   \item $y'\cos(x)+y \sin x=1, \ y(0)=1$
   \item $y'+2y = \begin{cases}
                     3x^2\cdot e^{5x} & \\
				     x^2-1 & \\
					 x\sin 2x & \\
					 x^2 \cos 3x
                   \end{cases} $
 \end{enumerate}
 \item Bernoulli
 \begin{enumerate}
   \item $x y'+y=\frac{\ln x}{y^3}$
   \item $5(1+x^2)y'=2x y+\frac{(1+x^2)^2}{y^4}$
   \item $y'-x^3 y^3=x y$
   \item $y'=4y-x y^2, \ x=0, y=2$
 \end{enumerate}
\end{enumerate}

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