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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x \]

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

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

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

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

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0 \]

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

\[ {}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y = 0 \]

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

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

\[ {}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {1+x}{x} \]

\[ {}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}} \]

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

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

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

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y = 0 \]

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

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