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

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \]

\[ {}2 z^{\prime \prime }+7 z^{\prime }-4 z = 0 \]

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

\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = 0 \]

\[ {}4 x^{\prime \prime }-20 x^{\prime }+21 x = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \]

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

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

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = {\mathrm e}^{2 t} \]

\[ {}x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \]

\[ {}x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

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

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

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

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

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

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

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

\[ {}\tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0 \]

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

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

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

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

\[ {}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \]

\[ {}\left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right ) \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

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

\[ {}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0 \]

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

\[ {}x^{2} z^{\prime \prime }+3 z^{\prime } x +4 z = 0 \]

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

\[ {}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = 0 \]

\[ {}3 x^{2} z^{\prime \prime }+5 z^{\prime } x -z = 0 \]

\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0 \]

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

\[ {}y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]

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

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

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2 \]

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

\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0 \]

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

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \]

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

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

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

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1 \]

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

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

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

\[ {}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

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

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

\[ {}\ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}} = 0 \]

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y \]

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

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0 \]

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

\[ {}\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y = 0 \]

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

\[ {}y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \]