\[ {}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+3 y_{2} \left (x \right )] \]

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

\[ {}\left [y_{1}^{\prime }\left (x \right ) = \frac {2 y_{1} \left (x \right )}{x}-\frac {y_{2} \left (x \right )}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}}, y_{2}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+1-6 x\right ] \]

\[ {}\left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x\right ] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )-2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+y_{2} \left (x \right )] \]

\[ {}\left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ] \]

\[ {}\left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ] \]

\[ {}\left [y_{1}^{\prime }\left (x \right ) = {\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}, y_{2}^{\prime }\left (x \right ) = \frac {y_{1} \left (x \right )}{\left (-2+x \right )^{2}}\right ] \]

\[ {}\left [y_{1}^{\prime }\left (x \right ) = {\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}, y_{2}^{\prime }\left (x \right ) = \frac {y_{1} \left (x \right )}{\left (-2+x \right )^{2}}\right ] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+5 \,{\mathrm e}^{x}, y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 \,{\mathrm e}^{-x}] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right )-2 y_{1} \left (x \right )+\sin \left (2 x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+y_{2} \left (x \right )-2 \cos \left (3 x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{3} \left (x \right )-y_{1} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 2 x y_{1} \left (x \right )-x^{2} y_{2} \left (x \right )+4 x, y_{2}^{\prime }\left (x \right ) = {\mathrm e}^{x} y_{1} \left (x \right )+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-\cos \left (3 x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+4 x -2, y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )+3 x] \]

\[ {}\left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}\right ] \]

\[ {}\left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x\right ] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+y_{2} \left (x \right )-3 y_{3} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 5 y_{1} \left (x \right )-5 y_{2} \left (x \right )-5 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+4 y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )-5 y_{2} \left (x \right )-3 y_{3} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 4 y_{1} \left (x \right )+6 y_{2} \left (x \right )+6 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+3 y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = -y_{1} \left (x \right )-4 y_{2} \left (x \right )-3 y_{3} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+2 y_{2} \left (x \right )-3 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{3} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = -2 y_{1} \left (x \right )-y_{2} \left (x \right )+y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )-2 y_{2} \left (x \right )-y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{2} \left (x \right )-2 y_{3} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+2 y_{2} \left (x \right )+4 y_{3} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+2 y_{2} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{3} \left (x \right )-4 y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 4 y_{3} \left (x \right )+3 y_{4} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-5 y_{3} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -2 y_{1} \left (x \right )+3 y_{2} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{3} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 2 y_{4} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right )+y_{4} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = y_{3} \left (x \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )] \]

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

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

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

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )-6, y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )+2] \]

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

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

\[ {}y^{\prime } = t^{4} y \]

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

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

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

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

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

\[ {}y^{\prime } = \frac {t}{y} \]

\[ {}y^{\prime } = \frac {t}{t^{2} y+y} \]

\[ {}y^{\prime } = t y^{\frac {1}{3}} \]

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

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

\[ {}y^{\prime } = y \left (1-y\right ) \]

\[ {}y^{\prime } = \frac {4 t}{1+3 y^{2}} \]

\[ {}v^{\prime } = t^{2} v-2-2 v+t^{2} \]

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

\[ {}y^{\prime } = \frac {{\mathrm e}^{t} y}{1+y^{2}} \]

\[ {}y^{\prime } = y^{2}-4 \]

\[ {}w^{\prime } = \frac {w}{t} \]

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

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

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

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

\[ {}y^{\prime } = t^{2} y^{3} \]

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

\[ {}y^{\prime } = \frac {t}{y-t^{2} y} \]

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

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

\[ {}x^{\prime } = \frac {t^{2}}{x+t^{3} x} \]

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

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

\[ {}y^{\prime } = \frac {1}{2 y+3} \]

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

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

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

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

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

\[ {}y^{\prime } = 4 y^{2} \]

\[ {}y^{\prime } = 2 y \left (1-y\right ) \]

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

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

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

\[ {}y^{\prime } = \left (y+\frac {1}{2}\right ) \left (y+t \right ) \]

\[ {}y^{\prime } = \left (t +1\right ) y \]

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]

\[ {}S^{\prime } = S^{3}-2 S^{2}+S \]

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

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

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

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

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

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