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

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

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

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

\[ {}\tan \relax (t ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \relax (t )+3 \cot \relax (t )\right ) x = 0 \]

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

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

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

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

\[ {}x^{\prime \prime }-4 x^{\prime } = \tan \relax (t ) \]

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

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

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

\[ {}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0 \]

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

\[ {}x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0 \]

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

\[ {}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \]

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

\[ {}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \]

\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}[x^{\prime }\relax (t ) = 5 x \relax (t )-4 y \relax (t )+{\mathrm e}^{3 t}, y^{\prime }\relax (t ) = x \relax (t )+y \relax (t )] \]

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

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

\[ {}[x^{\prime }\relax (t ) = 8 x \relax (t )+14 y \relax (t ), y^{\prime }\relax (t ) = 7 x \relax (t )+y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 8 x \relax (t )+14 y \relax (t ), y^{\prime }\relax (t ) = 7 x \relax (t )+y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t ), y^{\prime }\relax (t ) = -5 x \relax (t )-3 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 11 x \relax (t )-2 y \relax (t ), y^{\prime }\relax (t ) = 3 x \relax (t )+4 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+20 y \relax (t ), y^{\prime }\relax (t ) = 40 x \relax (t )-19 y \relax (t )] \]

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

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

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

\[ {}[x^{\prime }\relax (t ) = -11 x \relax (t )-2 y \relax (t ), y^{\prime }\relax (t ) = 13 x \relax (t )-9 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 7 x \relax (t )-5 y \relax (t ), y^{\prime }\relax (t ) = 10 x \relax (t )-3 y \relax (t )] \]

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

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

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

\[ {}[x^{\prime }\relax (t ) = 13 x \relax (t ), y^{\prime }\relax (t ) = 13 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 7 x \relax (t )-4 y \relax (t ), y^{\prime }\relax (t ) = x \relax (t )+3 y \relax (t )] \]

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

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

\[ {}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0 \]

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

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

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

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

\[ {}\sin \relax (x ) y+\cos \relax (x ) y^{\prime } = 1 \]

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

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

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

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

\[ {}{y^{\prime }}^{2} = 9 y^{4} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \left (x -5 y\right )^{\frac {1}{3}}+2 \]

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

\[ {}x^{\prime }+5 x = 10 t +2 \]

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

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

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

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

\[ {}x^{\prime }-x \cot \relax (t ) = 4 \sin \relax (t ) \]

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