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

\[ {}y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \]

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

\[ {}y^{\prime \prime }+25 y = 5 x^{2}+x \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \]

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

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \]

\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right ) \]

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

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

\[ {}y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \]

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \]

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \]

\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \]

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

\[ {}\frac {x^{\prime \prime }}{2} = -48 x \]

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \]

\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime \prime } = 5 x \]

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

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

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

\[ {}y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime }-y = 5 \]

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

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

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

\[ {}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2} \]

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

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

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

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime } = 0 \]

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

\[ {}y^{\prime \prime }+25 y = 0 \]

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

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

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

\[ {}y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 1 \]

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

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

\[ {}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 5 \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}} \]