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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x} \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right ) \]

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6 \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9 \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \]

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \]

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

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

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x} \]

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

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

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

\[ {}\left (1+x \right )^{3} y^{\prime \prime }+3 \left (1+x \right )^{2} y^{\prime }+\left (1+x \right ) y = 6 \ln \left (1+x \right ) \]

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

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

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

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 5 x^{4} \]

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \]

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

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

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

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

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

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

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

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

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

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

\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {x +6}{x^{2}} \]

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

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

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

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

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

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

\[ {}y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]

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

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

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

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

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

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

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

\[ {}x^{\prime \prime } = 1 \]

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

\[ {}x^{\prime \prime }-x^{\prime } = 1 \]

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

\[ {}x^{\prime \prime }+6 x^{\prime } = 12 t +2 \]

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

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

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

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