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

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y = \csc \relax (x ) \]

\[ {}x y^{\prime \prime }-\left (1+2 x \right ) y^{\prime }+2 y = 8 x^{2} {\mathrm e}^{2 x} \]

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 8 x^{4} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 15 \,{\mathrm e}^{3 x} \sqrt {x} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 4 \,{\mathrm e}^{2 x} \ln \relax (x ) \]

\[ {}4 x^{2} y^{\prime \prime }+y = \sqrt {x}\, \ln \relax (x ) \]

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

\[ {}y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-3 x} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = x^{2} \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = \sin \left (4 x \right ) \]

\[ {}y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y = 8 \,{\mathrm e}^{-x}+1 \]

\[ {}y^{\prime \prime }-4 y = 5 \,{\mathrm e}^{x} \]

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

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

\[ {}y^{\prime \prime }+x y = \sin \relax (x ) \]

\[ {}y^{\prime \prime }+4 y = \ln \relax (x ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 5 \,{\mathrm e}^{x} \]

\[ {}y^{\prime \prime }+y = \tan \relax (x ) \]

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

\[ {}y^{\prime }-2 y = 6 \,{\mathrm e}^{5 t} \]

\[ {}y^{\prime }+y = 8 \,{\mathrm e}^{3 t} \]

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

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

\[ {}y^{\prime }-y = 6 \cos \relax (t ) \]

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

\[ {}y^{\prime }+y = 5 \,{\mathrm e}^{t} \sin \relax (t ) \]

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

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

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

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 36 \]

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

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t} \]

\[ {}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t} \]

\[ {}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t} \]

\[ {}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 12-6 \,{\mathrm e}^{t} \]

\[ {}y^{\prime \prime }-y = 6 \cos \relax (t ) \]

\[ {}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }-y = 8 \sin \relax (t )-6 \cos \relax (t ) \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \relax (t ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 3 \cos \relax (t )+\sin \relax (t ) \]

\[ {}y^{\prime \prime }+4 y = 9 \sin \relax (t ) \]

\[ {}y^{\prime \prime }+y = 6 \cos \left (2 t \right ) \]

\[ {}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \]

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

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

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

\[ {}y^{\prime }-y = 4 \theta \left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right ) \]

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

\[ {}y^{\prime }+3 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

\[ {}y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \relax (t ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right . \]

\[ {}y^{\prime }-3 y = -10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \theta \left (t -a \right ) \]

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

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

\[ {}y^{\prime \prime }-4 y = \theta \left (t -1\right )-\theta \left (t -2\right ) \]

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \theta \left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \]

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 30 \theta \left (t -1\right ) {\mathrm e}^{1-t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \theta \left (t -3\right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \relax (t )+\theta \left (t -\frac {\pi }{2}\right ) \left (1+\cos \relax (t )\right ) \]

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

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

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

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

\[ {}y^{\prime }+4 y = 3 \delta \left (t -1\right ) \]

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

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

\[ {}y^{\prime \prime }-4 y = \delta \left (t -3\right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right ) \]

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]

\[ {}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]

\[ {}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \relax (t )+\delta \left (t -\frac {\pi }{6}\right ) \]

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

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

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

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

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

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

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

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

\[ {}\left (x^{2}-3\right ) y^{\prime \prime }-3 x y^{\prime }-5 y = 0 \]

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

\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \]

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

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