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

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

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

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

\[ {}\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+\frac {8}{9}\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\left (2 x^{2}+\frac {5}{9}\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\frac {3 y}{4} = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+8 \left (x^{2}-1\right ) y = 0 \]

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )+5 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right )+17 t] \]

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+7 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -3 x \left (t \right )-6 y \left (t \right )+6 z \left (t \right )] \]

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

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

\[ {}u^{\prime } = 4 t \ln \left (t \right ) \]

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

\[ {}T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime } = t^{2} x \]

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

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

\[ {}x^{\prime }+p x = q \]

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

\[ {}i^{\prime } = p \left (t \right ) i \]

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

\[ {}m v^{\prime } = -m g +k v^{2} \]

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

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

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

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

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

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

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

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