\[ {}2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right ) = 0 \]

\[ {}\left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0 \]

\[ {}\left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0 \]

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

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

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

\[ {}\left (c +2 b x +x^{2} a +y^{2}\right )^{2} y^{\prime \prime }+d y = 0 \]

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

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

\[ {}\left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right ) = 0 \]

\[ {}h \left (y\right ) y^{\prime \prime }+a D\left (h \right )\left (y\right ) {y^{\prime }}^{2}+j \left (y\right ) = 0 \]

\[ {}h \left (y\right ) y^{\prime \prime }-D\left (h \right )\left (y\right ) {y^{\prime }}^{2}-h \left (y\right )^{2} j \left (x , \frac {y^{\prime }}{h \left (y\right )}\right ) = 0 \]

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

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

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

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

\[ {}\left (\operatorname {f1} y^{\prime }+\operatorname {f2} y\right ) y^{\prime \prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f4} \left (x \right ) y y^{\prime }+\operatorname {f5} \left (x \right ) y^{2} = 0 \]

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

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

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

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

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

\[ {}x^{2} \left (2-9 x \right ) {y^{\prime \prime }}^{2}-6 x \left (1-6 x \right ) y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2} = 0 \]

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

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

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

\[ {}\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3}+32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3} = 0 \]

\[ {}\sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } = 3 \sqrt {y} \]

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

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

\[ {}m x^{\prime \prime } = f \left (x\right ) \]

\[ {}m x^{\prime \prime } = f \left (x^{\prime }\right ) \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } = \frac {a}{y^{3}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0 \]

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

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

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

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

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

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