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

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

\[ {}x^{\prime \prime }+\omega ^{2} x = \sin \left (\alpha t \right ) \]

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

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

\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \]

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

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

\[ {}x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

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

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

\[ {}x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t} \]

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

\[ {}x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x = \sin \left (t \right ) \]

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

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

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

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

\[ {}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \]

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

\[ {}y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]

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

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

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

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

\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \]

\[ {}y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x} \]

\[ {}x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1 \]

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

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

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

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

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

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

\[ {}y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = x \]

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

\[ {}x^{\prime \prime \prime \prime }+x = t^{3} \]

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

\[ {}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 y^{\prime \prime }-4 y^{\prime }+37 y = 0 \]

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

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

\[ {}4 y^{\prime \prime }-12 y^{\prime }+13 y = 0 \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

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

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

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

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

\[ {}3 y^{\prime \prime }+8 y^{\prime }-3 y = 0 \]

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

\[ {}4 y^{\prime \prime }+40 y^{\prime }+101 y = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+34 y = 0 \]

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

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

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

\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime } = 0 \]

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime } = 0 \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime } = 0 \]

\[ {}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 9 t \]

\[ {}4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1 \]

\[ {}4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t} \]

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

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-2 t} \]

\[ {}2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1 \]

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

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

\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right ) \]

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

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

\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \]

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

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right )\right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \]

\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right ) \]

\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]

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

\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \]

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

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

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