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

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

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

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

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

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

\[ {}y^{\prime \prime }+2 y = 6 x +4 \]

\[ {}y^{\prime \prime }+16 y = {\mathrm e}^{3 x} \]

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

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

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x} \]

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

\[ {}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2} \]

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x} \]

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

\[ {}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5 \]

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y = \sin \left (x \right )^{4} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right ) \]

\[ {}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right ) \]

\[ {}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \]

\[ {}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right ) \]

\[ {}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right ) \]

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right ) \]

\[ {}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right ) \]

\[ {}2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right ) \]

\[ {}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \]

\[ {}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right ) \]

\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]

\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]

\[ {}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right ) \]

\[ {}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t} \]

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

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

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}} \]

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

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

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

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

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

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

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

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

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (\frac {t}{4}\right ) \]

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (2 t \right ) \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \]

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

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \]

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

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

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

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k} \]

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}} \]

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 7 x^{\frac {3}{2}} {\mathrm e}^{x} \]

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

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