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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\{x^{\prime \prime }\relax (t )+y^{\prime }\relax (t )-2 y \relax (t ) = {\mathrm e}^{2 t}, 2 x^{\prime }\relax (t )+y^{\prime }\relax (t )-3 x \relax (t ) = 0\} \]

\[ {}\{x^{\prime }\relax (t )-y^{\prime }\relax (t )+x \relax (t ) = 2 t, x^{\prime \prime }\relax (t )+y^{\prime }\relax (t )-9 x \relax (t )+3 y \relax (t ) = \sin \left (2 t \right )\} \]

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

\[ {}\{t x^{\prime \prime }\relax (t )+2 x^{\prime }\relax (t )+x \relax (t ) t = 0, t x^{\prime }\relax (t )-t y^{\prime }\relax (t )-2 y \relax (t ) = 0\} \]

\[ {}\{x^{\prime \prime }\relax (t )+a y \relax (t ) = 0, y^{\prime \prime }\relax (t )-a^{2} y \relax (t ) = 0\} \]

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

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

\[ {}\{x^{\prime \prime }\relax (t )+x \relax (t )+y \relax (t ) = -5, y^{\prime \prime }\relax (t )-4 x \relax (t )-3 y \relax (t ) = -3\} \]

\[ {}\left \{x^{\prime \prime }\relax (t ) = \left (3 \left (\cos ^{2}\left (a t +b \right )\right )-1\right ) c^{2} x \relax (t )+\frac {3 c^{2} y \relax (t ) \sin \left (2 a t b \right )}{2}, y^{\prime \prime }\relax (t ) = \left (3 \left (\sin ^{2}\left (a t +b \right )\right )-1\right ) c^{2} y \relax (t )+\frac {3 c^{2} x \relax (t ) \sin \left (2 a t b \right )}{2}\right \} \]

\[ {}\{x^{\prime \prime }\relax (t )+6 x \relax (t )+7 y \relax (t ) = 0, y^{\prime \prime }\relax (t )+3 x \relax (t )+2 y \relax (t ) = 2 t\} \]

\[ {}\{x^{\prime \prime }\relax (t )-a y^{\prime }\relax (t )+b x \relax (t ) = 0, y^{\prime \prime }\relax (t )+a x^{\prime }\relax (t )+b y \relax (t ) = 0\} \]

\[ {}\{a_{1} x^{\prime \prime }\relax (t )+b_{1} x^{\prime }\relax (t )+c_{1} x \relax (t )-A y^{\prime }\relax (t ) = B \,{\mathrm e}^{i \omega t}, a_{2} y^{\prime \prime }\relax (t )+b_{2} y^{\prime }\relax (t )+c_{2} y \relax (t )+A x^{\prime }\relax (t ) = 0\} \]

\[ {}\{x^{\prime \prime }\relax (t )+a \left (x^{\prime }\relax (t )-y^{\prime }\relax (t )\right )+b_{1} x \relax (t ) = c_{1} {\mathrm e}^{i \omega t}, y^{\prime \prime }\relax (t )+a \left (y^{\prime }\relax (t )-x^{\prime }\relax (t )\right )+b_{2} y \relax (t ) = c_{2} {\mathrm e}^{i \omega t}\} \]

\[ {}\{\mathit {a11} x^{\prime \prime }\relax (t )+\mathit {b11} x^{\prime }\relax (t )+\mathit {c11} x \relax (t )+\mathit {a12} y^{\prime \prime }\relax (t )+\mathit {b12} y^{\prime }\relax (t )+\mathit {c12} y \relax (t ) = 0, \mathit {a21} x^{\prime \prime }\relax (t )+\mathit {b21} x^{\prime }\relax (t )+\mathit {c21} x \relax (t )+\mathit {a22} y^{\prime \prime }\relax (t )+\mathit {b22} y^{\prime }\relax (t )+\mathit {c22} y \relax (t ) = 0\} \]

\[ {}\{y^{\prime \prime \prime }\relax (t )-y^{\prime \prime }\relax (t )+2 x^{\prime }\relax (t )-x \relax (t ) = t, x^{\prime \prime }\relax (t )-2 x^{\prime }\relax (t )-y^{\prime }\relax (t )+y \relax (t ) = 0\} \]

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

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

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

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

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

\[ {}\{x^{\prime }\relax (t )-y \relax (t )+z \relax (t ) = 0, y^{\prime }\relax (t )-x \relax (t )-y \relax (t ) = t, z^{\prime }\relax (t )-x \relax (t )-z \relax (t ) = t\} \]

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

\[ {}\{x^{\prime }\relax (t ) = c y \relax (t )-b z \relax (t ), y^{\prime }\relax (t ) = a z \relax (t )-c x \relax (t ), z^{\prime }\relax (t ) = b x \relax (t )-a y \relax (t )\} \]

\[ {}\{x^{\prime }\relax (t ) = h \relax (t ) y \relax (t )-g \relax (t ) z \relax (t ), y^{\prime }\relax (t ) = f \relax (t ) z \relax (t )-h \relax (t ) x \relax (t ), z^{\prime }\relax (t ) = x \relax (t ) g \relax (t )-y \relax (t ) f \relax (t )\} \]

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

\[ {}\{x^{\prime }\relax (t ) = -3 x \relax (t )+48 y \relax (t )-28 z \relax (t ), y^{\prime }\relax (t ) = -4 x \relax (t )+40 y \relax (t )-22 z \relax (t ), z^{\prime }\relax (t ) = -6 x \relax (t )+57 y \relax (t )-31 z \relax (t )\} \]

\[ {}\{x^{\prime }\relax (t ) = 6 x \relax (t )-72 y \relax (t )+44 z \relax (t ), y^{\prime }\relax (t ) = 4 x \relax (t )-4 y \relax (t )+26 z \relax (t ), z^{\prime }\relax (t ) = 6 x \relax (t )-63 y \relax (t )+38 z \relax (t )\} \]

\[ {}\{x^{\prime }\relax (t ) = a x \relax (t )+g y \relax (t )+\beta z \relax (t ), y^{\prime }\relax (t ) = g x \relax (t )+b y \relax (t )+\alpha z \relax (t ), z^{\prime }\relax (t ) = \beta x \relax (t )+\alpha y \relax (t )+c z \relax (t )\} \]

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

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

\[ {}\{x_{1}^{\prime }\relax (t ) = a x_{2} \relax (t )+b x_{3} \relax (t ) \cos \left (c t \right )+b x_{4} \relax (t ) \sin \left (c t \right ), x_{2}^{\prime }\relax (t ) = -a x_{1} \relax (t )+b x_{3} \relax (t ) \sin \left (c t \right )-b x_{4} \relax (t ) \cos \left (c t \right ), x_{3}^{\prime }\relax (t ) = -b x_{1} \relax (t ) \cos \left (c t \right )-b x_{2} \relax (t ) \sin \left (c t \right )+a x_{4} \relax (t ), x_{4}^{\prime }\relax (t ) = -b x_{1} \relax (t ) \sin \left (c t \right )+b x_{2} \relax (t ) \cos \left (c t \right )-a x_{3} \relax (t )\} \]

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

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

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

\[ {}\{x^{\prime }\relax (t ) = h \left (a -x \relax (t )\right ) \left (c -x \relax (t )-y \relax (t )\right ), y^{\prime }\relax (t ) = k \left (b -y \relax (t )\right ) \left (c -x \relax (t )-y \relax (t )\right )\} \]

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

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

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

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

\[ {}\left \{x^{\prime }\relax (t ) = -y \relax (t ) \left (x \relax (t )^{2}+y \relax (t )^{2}\right ), y^{\prime }\relax (t ) = \left \{\begin {array}{cc} x \relax (t )^{2}+y \relax (t )^{2} & 2 x \relax (t )\le x \relax (t )^{2}+y \relax (t )^{2} \\ \left (\frac {x \relax (t )}{2}-\frac {y \relax (t )^{2}}{2 x \relax (t )}\right ) \left (x \relax (t )^{2}+y \relax (t )^{2}\right ) & \mathit {otherwise} \end {array}\right .\right \} \]