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

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

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

\[ {}y^{\prime \prime }+9 y = 1 \]

\[ {}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \]

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

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

\[ {}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \]

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]

\[ {}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \]

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

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

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t} \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t} \]

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = -8 \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2} \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t} \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t} \]

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

\[ {}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t} \]

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

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right ) \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \]

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

\[ {}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right ) \]

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

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

\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right ) \]

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right ) \]

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

\[ {}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \]

\[ {}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \]

\[ {}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \]

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

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

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

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