\[ {}\frac {y^{\prime }}{y}+p \relax (x ) \ln \relax (y) = q \relax (x ) \]

\[ {}\frac {y^{\prime }}{y}-\frac {2 \ln \relax (y)}{x} = \frac {1-2 \ln \relax (x )}{x} \]

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

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

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

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

\[ {}2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime } = 0 \]

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

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

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

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

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

\[ {}2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime } = 0 \]

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

\[ {}\sin \relax (y)+y \cos \relax (x )+\left (x \cos \relax (y)+\sin \relax (x )\right ) y^{\prime } = 0 \]

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

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]

\[ {}y^{\prime \prime }-36 y = 0 \]

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

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

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y = 0 \]

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y = 0 \]

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

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 0 \]

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

\[ {}y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y = 0 \]

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \]

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]

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

\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 x y^{\prime } = 0 \]

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x} \]

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

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

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 24 \,{\mathrm e}^{-3 x} \]

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

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

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

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 4 x^{2} \]

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

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

\[ {}y^{\prime \prime }+9 y = 5 \cos \left (2 x \right ) \]

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

\[ {}y^{\prime \prime }+y^{\prime }-2 y = -10 \sin \relax (x ) \]

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

\[ {}y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x} \]

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

\[ {}y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime } = 5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \]

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

\[ {}y^{\prime \prime }+6 y = \left (\sin ^{2}\relax (x )\right ) \left (\cos ^{2}\relax (x )\right ) \]

\[ {}y^{\prime \prime }-16 y = 20 \cos \left (4 x \right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 50 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }-y = 10 \,{\mathrm e}^{2 x} \cos \relax (x ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 40 \left (\sin ^{2}\relax (x )\right ) \]

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

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

\[ {}y^{\prime \prime }-4 y = 100 x \,{\mathrm e}^{x} \sin \relax (x ) \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \]

\[ {}y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \relax (x ) \]

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

\[ {}y^{\prime \prime }+9 y = 18 \left (\sec ^{3}\left (3 x \right )\right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \]

\[ {}y^{\prime \prime }-4 y = \frac {8}{{\mathrm e}^{2 x}+1} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \tan \relax (x ) \]

\[ {}y^{\prime \prime }+9 y = \frac {36}{4-\left (\cos ^{2}\left (3 x \right )\right )} \]

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \left (\sec ^{2}\left (2 x \right )\right ) \]

\[ {}y^{\prime \prime }+y = \sec \relax (x )+4 \,{\mathrm e}^{x} \]

\[ {}y^{\prime \prime }+y = \csc \relax (x )+2 x^{2}+5 x +1 \]

\[ {}y^{\prime \prime }-y = 2 \tanh \relax (x ) \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {4 \,{\mathrm e}^{x} \ln \relax (x )}{x^{3}} \]

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

\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin ^{2}\left (4 x \right )} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1 \]

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \relax (x )+25 \cos \relax (x ) \]

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

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 36 \,{\mathrm e}^{2 x} \ln \relax (x ) \]

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

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

\[ {}y^{\prime \prime }-9 y = F \relax (x ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = F \relax (x ) \]

\[ {}y^{\prime \prime }+y^{\prime }-2 y = F \relax (x ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = F \relax (x ) \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 9 \ln \relax (x ) \]

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 8 x \ln \relax (x )^{2} \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \relax (x ) \]

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

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

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