\[ {}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+2 x_{2} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{-t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 t] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 16 x_{1} \left (t \right )-5 x_{2} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+5 x_{2} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-8, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+3] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-8, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+3] \]

\[ {}y^{\prime } = {\mathrm e}^{3 x}+\sin \left (x \right ) \]

\[ {}y^{\prime \prime } = 2+x \]

\[ {}y^{\prime \prime \prime } = x^{2} \]

\[ {}y^{\prime }+\cos \left (x \right ) y = 0 \]

\[ {}y^{\prime }+\cos \left (x \right ) y = \cos \left (x \right ) \sin \left (x \right ) \]

\[ {}y^{\prime \prime }-y = 0 \]

\[ {}y^{\prime \prime }+4 y = 0 \]

\[ {}y^{\prime \prime }+k^{2} y = 0 \]

\[ {}y^{\prime }+5 y = 2 \]

\[ {}y^{\prime \prime } = 3 x +1 \]

\[ {}y^{\prime } = k y \]

\[ {}y^{\prime }-2 y = 1 \]

\[ {}y^{\prime }+y = {\mathrm e}^{x} \]

\[ {}y^{\prime }-2 y = x^{2}+x \]

\[ {}3 y^{\prime }+y = 2 \,{\mathrm e}^{-x} \]

\[ {}y^{\prime }+3 y = {\mathrm e}^{i x} \]

\[ {}y^{\prime }+i y = x \]

\[ {}L y^{\prime }+R y = E \]

\[ {}L y^{\prime }+R y = E \sin \left (\omega x \right ) \]

\[ {}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x} \]

\[ {}y^{\prime }+a y = b \left (x \right ) \]

\[ {}y^{\prime }+2 x y = x \]

\[ {}x y^{\prime }+y = 3 x^{3}-1 \]

\[ {}y^{\prime }+{\mathrm e}^{x} y = 3 \,{\mathrm e}^{x} \]

\[ {}y^{\prime }-\tan \left (x \right ) y = {\mathrm e}^{\sin \left (x \right )} \]

\[ {}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}} \]

\[ {}y^{\prime }+\cos \left (x \right ) y = {\mathrm e}^{-\sin \left (x \right )} \]

\[ {}x^{2} y^{\prime }+2 x y = 1 \]

\[ {}y^{\prime }+2 y = b \left (x \right ) \]

\[ {}y^{\prime } = y+1 \]

\[ {}y^{\prime } = 1+y^{2} \]

\[ {}y^{\prime } = 1+y^{2} \]

\[ {}y^{\prime \prime }-4 y = 0 \]

\[ {}3 y^{\prime \prime }+2 y = 0 \]

\[ {}y^{\prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime } = 0 \]

\[ {}y^{\prime \prime }+2 i y^{\prime }+y = 0 \]

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]

\[ {}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \]

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]

\[ {}y^{\prime \prime }+y = 0 \]

\[ {}y^{\prime \prime }+y = 0 \]

\[ {}y^{\prime \prime }+y = 0 \]

\[ {}y^{\prime \prime }+y = 0 \]

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]

\[ {}y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y = 0 \]

\[ {}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \]

\[ {}y^{\prime \prime }+10 y = 0 \]

\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \]

\[ {}y^{\prime \prime }+9 y = \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \]

\[ {}y^{\prime \prime }+2 i y^{\prime }+y = x \]

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2} \]

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

\[ {}y^{\prime \prime }+y = 2 \sin \left (2 x \right ) \sin \left (x \right ) \]

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

\[ {}4 y^{\prime \prime }-y = {\mathrm e}^{x} \]

\[ {}6 y^{\prime \prime }+5 y^{\prime }-6 y = x \]

\[ {}y^{\prime \prime }+\omega ^{2} y = A \cos \left (\omega x \right ) \]

\[ {}y^{\prime \prime \prime }-8 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime } = 0 \]

\[ {}y^{\prime \prime \prime }-i y^{\prime \prime }+4 y^{\prime }-4 i y = 0 \]

\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-16 y = 0 \]

\[ {}y^{\prime \prime \prime }-3 y^{\prime }-2 y = 0 \]

\[ {}y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y = 0 \]

\[ {}y^{\prime \prime \prime }-4 y^{\prime } = 0 \]

\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime }-y^{\prime }+y = 0 \]

\[ {}y^{\prime \prime }+y = 0 \]

\[ {}y^{\prime \prime }-y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-y = 0 \]

\[ {}y^{\left (5\right )}+2 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \]

\[ {}y^{\prime \prime \prime }+y = 0 \]

\[ {}y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y = 0 \]

\[ {}y^{\prime \prime }-2 i y^{\prime }-y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-k^{4} y = 0 \]

\[ {}y^{\prime \prime \prime }-y = x \]

\[ {}y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x} \]

\[ {}y^{\prime \prime \prime \prime }+16 y = \cos \left (x \right ) \]

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x} \]

\[ {}y^{\prime \prime \prime \prime }-y = \cos \left (x \right ) \]

\[ {}y^{\prime \prime }-2 i y^{\prime }-y = {\mathrm e}^{i x}-2 \,{\mathrm e}^{-i x} \]

\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \]

\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime }-4 y = 3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2}+\cos \left (x \right ) \]