\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}-4 y^{2} = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}3 y y^{\prime \prime }-5 {y^{\prime }}^{2} = 0 \]

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

\[ {}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3} = 0 \]

\[ {}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+a y^{3}+b y^{2}+c y = 0 \]

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

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

\[ {}12 y y^{\prime \prime }-15 {y^{\prime }}^{2}+8 y^{3} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2} = 0 \]

\[ {}\operatorname {f0} \left (x \right ) y y^{\prime \prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f3} \left (x \right ) y^{2} = 0 \]

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

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

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

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

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

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

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

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

\[ {}-2 y \left (1-y\right ) y^{\prime \prime }+\left (-3 y+1\right ) {y^{\prime }}^{2}-4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+\left (1-y\right )^{3} \left (\operatorname {f0} \left (x \right )^{2} y^{2}-\operatorname {f1} \left (x \right )^{2}\right )+4 y^{2} \left (1-y\right ) \left (f \left (x \right )^{2}-g \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-a \,x^{n} y = 0 \]

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

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

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

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

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

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