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

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

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

\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

\[ {}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-2 y = 4 x -8 \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2} \]

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2} \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

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

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

\[ {}\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{3} x^{\prime \prime }+1 = 0 \]

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

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

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