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

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

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

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

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

\[ {}y^{\prime \prime } \left (2+x \right )^{5} = 1 \]

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

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

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

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

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

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

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

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

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

\[ {}3 y^{\prime \prime }-2 y^{\prime }-8 y = 0 \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \]

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

\[ {}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0 \]

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

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

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

\[ {}y^{\prime \prime }-7 y^{\prime } = \left (-1+x \right )^{2} \]

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

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

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x} \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \]

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+8 y^{\prime } = 8 x \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x} \]

\[ {}7 y^{\prime \prime }-y^{\prime } = 14 x \]

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

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x} \]

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right ) \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 10 \cos \left (x \right ) {\mathrm e}^{-2 x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right ) \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right ) \]

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right ) \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 1+8 \cos \left (x \right )+{\mathrm e}^{2 x} \]

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1 \]

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \]

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2 \]

\[ {}y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x} \]