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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \]

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

\[ {}y^{\prime \prime } \left (2+x \right )^{5} = 1 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2} \]

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

\[ {}3 y^{\prime \prime }-2 y^{\prime }-8 y = 0 \]

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

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

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

\[ {}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0 \]

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

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

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

\[ {}y^{\prime \prime }-7 y^{\prime } = \left (-1+x \right )^{2} \]

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

\[ {}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x} \]

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x} \]

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x} \]

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

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

\[ {}y^{\prime \prime }+25 y = \cos \left (5 x \right ) \]

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

\[ {}y^{\prime \prime }+16 y = \sin \left (4 x +\alpha \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime }-4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 x} \cos \left (2 x \right ) \]

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

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

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

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

\[ {}y^{\prime \prime }+9 y = 9 \]

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

\[ {}y^{\prime \prime }+8 y^{\prime } = 8 x \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x} \]

\[ {}7 y^{\prime \prime }-y^{\prime } = 14 x \]

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

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x} \]

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right ) \]

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \sin \left (2 x \right ) {\mathrm e}^{-x} \]

\[ {}y^{\prime \prime }+a^{2} y = 2 \cos \left (m x \right )+3 \sin \left (m x \right ) \]

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

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