\[ {}x^{\prime \prime }+9 x = 0 \]

\[ {}10 x^{\prime \prime }+\frac {x}{10} = 0 \]

\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = 0 \]

\[ {}\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0 \]

\[ {}\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x = 0 \]

\[ {}4 x^{\prime \prime }+2 x^{\prime }+8 x = 0 \]

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = 0 \]

\[ {}x^{\prime \prime }+4 x^{\prime }+20 x = 0 \]

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \]

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

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

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

\[ {}x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right ) \]

\[ {}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right ) \]

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right ) \]

\[ {}[x^{\prime }\left (t \right ) = 6, y^{\prime }\left (t \right ) = \cos \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = 0, y^{\prime }\left (t \right ) = -2 y \left (t \right )] \]

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = 8 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+6 y \left (t \right )] \]

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

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

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

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

\[ {}x^{\prime \prime }-3 x^{\prime }+4 x = 0 \]

\[ {}x^{\prime \prime }+6 x^{\prime }+9 x = 0 \]

\[ {}x^{\prime \prime }+16 x = t \sin \left (t \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {1}{x} \]

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

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

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

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

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

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

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

\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \]

\[ {}1+y^{2}+x y y^{\prime } = 0 \]

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

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

\[ {}x \sqrt {1+y^{2}}+y y^{\prime } \sqrt {x^{2}+1} = 0 \]

\[ {}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0 \]

\[ {}{\mathrm e}^{-y} y^{\prime } = 1 \]

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

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

\[ {}{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right ) = 0 \]

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

\[ {}{\mathrm e}^{x} \sin \left (y\right )^{3}+\left ({\mathrm e}^{2 x}+1\right ) \cos \left (y\right ) y^{\prime } = 0 \]

\[ {}y^{2} \sin \left (x \right )+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime } = 0 \]

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

\[ {}y^{\prime } = a x +b y+c \]

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

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

\[ {}a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0 \]

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

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

\[ {}{\mathrm e}^{y^{\prime }} = 1 \]

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

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

\[ {}\tan \left (y^{\prime }\right ) = 0 \]

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

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

\[ {}x^{2} y^{\prime } \cos \left (y\right )+1 = 0 \]

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