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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 y^{2} y^{\prime \prime \prime }-18 y y^{\prime } y^{\prime \prime }+15 {y^{\prime }}^{3} = 0 \]

\[ {}9 y^{2} y^{\prime \prime \prime }-45 y y^{\prime } y^{\prime \prime }+40 {y^{\prime }}^{3} = 0 \]

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

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

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

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

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

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

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

\[ {}9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime } = 0 \]

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

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

\[ {}\{x^{\prime }\left (t \right ) = a x \left (t \right ), y^{\prime }\left (t \right ) = b\} \]

\[ {}\{x^{\prime }\left (t \right ) = a y \left (t \right ), y^{\prime }\left (t \right ) = -a x \left (t \right )\} \]

\[ {}\{x^{\prime }\left (t \right ) = a y \left (t \right ), y^{\prime }\left (t \right ) = b x \left (t \right )\} \]

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

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

\[ {}\{a x^{\prime }\left (t \right )+b y^{\prime }\left (t \right ) = \alpha x \left (t \right )+\beta y \left (t \right ), b x^{\prime }\left (t \right )-a y^{\prime }\left (t \right ) = \beta x \left (t \right )-\alpha y \left (t \right )\} \]

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

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

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

\[ {}\{x^{\prime }\left (t \right ) = a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1}, y^{\prime }\left (t \right ) = a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2}\} \]

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

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

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

\[ {}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{2 t}+t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right ) = {\mathrm e}^{t}-1] \]

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

\[ {}[4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+2 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+x \left (t \right )+24 y \left (t \right ) = 3] \]

\[ {}[4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+11 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+8 x \left (t \right )+24 y \left (t \right ) = {\mathrm e}^{2 t}] \]

\[ {}[4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+44 x \left (t \right )+49 y \left (t \right ) = t, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+34 x \left (t \right )+38 y \left (t \right ) = {\mathrm e}^{t}] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right ) f \left (t \right )+y \left (t \right ) g \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right ) g \left (t \right )+y \left (t \right ) f \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right )+\left (a x \left (t \right )+b y \left (t \right )\right ) f \left (t \right ) = g \left (t \right ), y^{\prime }\left (t \right )+\left (c x \left (t \right )+d y \left (t \right )\right ) f \left (t \right ) = h \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right ) \cos \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right ) {\mathrm e}^{-\sin \left (t \right )}] \]

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