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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \]

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \]

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

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right ) \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2} \]

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]

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

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

\[ {}5 y^{\prime \prime }+2 y^{\prime }+4 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \]

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

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