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\section*{Extra Opgaven}

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Los de volgende beginwaardeproblemen op:
\begin{itemize}
\item[(a)] $y'=\cos t$, $y(\pi/6)=2$.
\item[(b)] $y'=e^{2t}$, $y(1)=0$.
\item[(c)] $y'=10y$, $y(1)=2$.
\item[(d)] $y'=3\sin 3t$, $y(\pi/6)=1$.
\item[(e)] $y\,dy=x\,dx$, $y(1)=-2$.
\end{itemize}
Geef de algemene oplossing van:
\begin{itemize}
\item[(f)] $y\,dy=x^2\,dx$.
\item[(g)] $y'=-x/y$.
\end{itemize}

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{\sc Antwoorden:}
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\begin{itemize}
\item[(a)] $y(t)=\sin t+3/2$.
\item[(b)] $y(t)=e^{2t}/2-e^2/2$.
\item[(c)] $y(t)=2e^{10(t-1)}$.
\item[(d)] $y(t)=-\cos 3t+1$.
\item[(e)] $y(x)=-\sqrt{3-x^2}$.
\item[(f)] $y^2/2=x^3/3 +C$.
\item[(g)] $x^2+y^2=C$, $C>0$.
\end{itemize}

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