\[ {}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \]

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \]

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-\frac {x y^{\prime }}{-1+x}+\frac {y}{-1+x} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y = \sec \left (2 x \right ) \]

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

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

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

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

\[ {}y^{\prime \prime }+y = -8 \sin \left (3 x \right ) \]

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

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

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

\[ {}y^{\prime \prime }+9 y = -3 \cos \left (2 x \right ) \]

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

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }-5 y = 1 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t} \]

\[ {}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \]

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

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]

\[ {}16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0 \]

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \]

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0 \]

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

\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \]

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