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

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x} \]

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

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

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

\[ {}y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x} \]

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right ) \]

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

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right ) \]

\[ {}5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime }+9 y = 30 \sin \left (3 x \right ) \]

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

\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \]

\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \]

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

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x} \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \]

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3} \]

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 x^{2} \ln \relax (x ) \]

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

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

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

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

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

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

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

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

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

\[ {}x \ln \relax (y) y^{\prime }-y \ln \relax (x ) = 0 \]

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

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \relax (x ) \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 26 \,{\mathrm e}^{3 x} \]

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

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

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

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

\[ {}\left (x \cos \relax (y)-{\mathrm e}^{-\sin \relax (y)}\right ) y^{\prime }+1 = 0 \]

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

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

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

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y = 0 \]

\[ {}\sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\left (\sin ^{2}\left (\theta \right )\right ) = r \left (\cos ^{2}\left (\theta \right )\right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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