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\raggedright





\includegraphics{logo_unze}


\vspace*{-25mm}
\hspace*{30mm}
\textbf{Univerzitet u Zenici}\\
\hspace*{30mm}
\textbf{Politehnički fakultet}\\
\hspace*{30mm}
Odsjek: Građevinarstvo\\
\hspace*{30mm}
Primjer parcijalnog ispita\\


\vspace*{5mm}
\renewcommand{\thesection}{}
\section{\centerline{Prvi parcijalni iz Inžinjerske matematike III}}




\vspace*{5mm}
{\large \textbf{Pravila:} Svaku formulu koju mislite koristit, u sva 4 zadatka, obavezno napisati, kao i značenja simbola iz formule. Ispit pisati isključivo hemiskom olovkom plave ili crne tinte. Prije rješenja prepisati postavku (tekst) zadatka.}\\




\begin{zad}
Metodom svođenja na jednu diferencijalnu jednačinu višeg reda rješiti sljedeći sistem
\begin{eqnarray}
\dot{x}-\ddot{y}+y & = & \cos t \nonumber\\
x+\dot{y}-y & = & e^{3t} \nonumber
\end{eqnarray}
\end{zad}



\begin{zad}
Metodom varijacije konstanti (ili metodom pogađanja partikularnog rješenja) rješiti dati sistem linearnih jednačina
\begin{eqnarray}
\dot{x} & = & 3x+ y+\cos t \nonumber\\
\dot{y} & = & -x+y-\cos t \nonumber
\end{eqnarray}
\end{zad}



\begin{zad}
Primjenom Laplaceove transformacije izračunati integral $\displaystyle{
\int_0^\infty te^{-2t}\cos t \dt
}$.
\end{zad}




\begin{zad}
Primjenom Laplaceove transformacije rješiti diferencijalnu jednačinu
$$
ty''+(t-2)y'+y=0;\,\,\,\,\,y(0)=0,\,\,\,\,\,y'(0)=0.
$$
\end{zad}


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\centerline{
Zadaci su skinuti sa stranice 
\underline{pf.unze.ba\slash nabokov}.}
\centerline{
Za uočene greške pisati na {\it infoarrt@gmail.com}
}




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