\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \]

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \]

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \]

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

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

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 x^{2} \ln \left (x \right ) \]

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

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

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

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

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