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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \relax (x ) \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y = 8 \cos \relax (x ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right ) \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}r^{\prime \prime } = -\frac {k}{r^{2}} \]

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

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

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

\[ {}r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \]

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

\[ {}y y^{\prime \prime }-3 \left (y^{\prime }\right )^{2} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0 \]

\[ {}y^{\prime }-\left (y-f \relax (x )\right ) \left (y-g \relax (x )\right ) \left (y-\frac {a f \relax (x )+b g \relax (x )}{a +b}\right ) h \relax (x )-\frac {f^{\prime }\relax (x ) \left (y-g \relax (x )\right )}{f \relax (x )-g \relax (x )}-\frac {g^{\prime }\relax (x ) \left (y-f \relax (x )\right )}{g \relax (x )-f \relax (x )} = 0 \]

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

\[ {}\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2} = 0 \]

\[ {}y^{\prime }+y \tan \relax (x ) = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime }+b^{2} y^{2} = a^{2} \]

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

\[ {}\sin \relax (x ) \cos \relax (y) = \cos \relax (x ) \sin \relax (y) y^{\prime } \]

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

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

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

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

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

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

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

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

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

\[ {}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0 \]

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

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

\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (-n +1\right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (-n +1\right ) x y = 0 \]

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