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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y \]

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

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

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

\[ {}{y^{\prime }}^{2}-5 y^{\prime }+6 = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}16 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0 \]

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

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

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

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

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

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

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

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

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

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

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