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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \]

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

\[ {}y^{\prime \prime }+9 y = 8 \cos \left (x \right ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }+6 y = 0 \]

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

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

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

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

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

\[ {}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0 \]

\[ {}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0 \]

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

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

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y = 0 \]

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

\[ {}y^{\prime \prime }-4 y^{\prime } = 10 \]

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x} \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x} \]

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

\[ {}y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x} \]

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right ) \]

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

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right ) \]

\[ {}5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime }+9 y = 30 \sin \left (3 x \right ) \]

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

\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \]

\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \]

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x} \]

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

\[ {}y^{\prime \prime }+y = x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \]

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

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \]

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 26 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \cos \left (x \right ) {\mathrm e}^{-2 x} \]

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y = 0 \]

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

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

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

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

\[ {}x^{\prime \prime }-\omega ^{2} x = 0 \]

\[ {}x^{\prime \prime \prime }-x^{\prime \prime }+x^{\prime }-x = 0 \]

\[ {}x^{\prime \prime }+42 x^{\prime }+x = 0 \]

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

\[ {}x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0 \]

\[ {}x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \]

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

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

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

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