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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y = 0 \]

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

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \]

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

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

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

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

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

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

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

\[ {}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \]

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

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

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \]

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

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

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

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

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

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

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

\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \]

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

\[ {}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0 \]

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

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

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y = 0 \]

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

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

\[ {}\left (x -1\right ) y^{\prime \prime }+3 y = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5 \]

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

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

\[ {}y^{\prime }+6 y = {\mathrm e}^{4 t} \]

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

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

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

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

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{t} \]

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \]

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

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \]

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

\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = 0 \]

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \]

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

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

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

\[ {}y^{\prime \prime }+4 y = \sin \left (t \right ) \operatorname {Heaviside}\left (-2 \pi +t \right ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right ) \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \]

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

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

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

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

\[ {}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+16 y = \delta \left (-2 \pi +t \right ) \]