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

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

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

\[ {}4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+x y = 0 \]

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y = 0 \]

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

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

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

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

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

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

\[ {}x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0 \]

\[ {}x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y = 0 \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0 \]

\[ {}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y = 0 \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+5 x \right ) y = 0 \]

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

\[ {}9 x^{2} y^{\prime \prime }-15 x y^{\prime }+7 \left (x +1\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +7\right ) y^{\prime }+2 \left (x +5\right ) y = 0 \]

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

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }-18 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 x y = 0 \]

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

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

\[ {}x \left (-2 x +1\right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+18 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]

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

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

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

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

\[ {}[x^{\prime }\relax (t ) = 6 x \relax (t )-7 y \relax (t )+10, y^{\prime }\relax (t ) = x \relax (t )-2 y \relax (t )-2 \,{\mathrm e}^{t}] \]

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

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

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

\[ {}y^{\prime } = \left (5+\frac {\sec \relax (x )}{x}\right ) \left (\sin \relax (y)+y\right ) \]

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

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

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

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

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