\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \]

\[ {}y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (-1+t \right ) \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \]

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

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (-1+t \right ) \]

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (-1+t \right ) \]

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y = 8 \]

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

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \]

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

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (-1+t \right ) \]

\[ {}y^{\prime \prime \prime \prime }-16 y = 32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right ) \]

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

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

\[ {}y^{\prime \prime }-3 y^{\prime }-7 y = 4 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } = 9 y \]

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

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

\[ {}y^{\prime \prime }+12 y = 7 y^{\prime } \]

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

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

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

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

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

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

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

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

\[ {}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 0 \]

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

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0 \]

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = x \]

\[ {}s^{\prime \prime }-a^{2} s = t +1 \]

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \]

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

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

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

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

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3 \]

\[ {}y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right ) \]

\[ {}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 8 \cos \left (a x \right ) \]

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

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

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

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

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

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

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

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

\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime } = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y = 31 \]

\[ {}y^{\prime \prime }+9 y = 27 x +18 \]

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

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

\[ {}y^{\prime \prime \prime \prime }-16 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime } = 0 \]

\[ {}36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0 \]

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

\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0 \]

\[ {}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0 \]

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

\[ {}y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0 \]

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

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \]

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

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 \,{\mathrm e}^{x} x^{2} \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \]