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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (2+x \right ) {\mathrm e}^{4 x} \]

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x} \]

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