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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right ) \]

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

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

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

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

\[ {}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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