$$\{x^{\prime }(t)=-y(t)+\left(\{\begin{array}{cc}x(t)(x(t{)}^2+y(t{)}^2-1)\sin \left(\frac{1}{x(t{)}^2+y(t{)}^2}\right)& x(t{)}^2+y(t{)}^2\ne 1\\ 0& \mathit{otherwise}\end{array}\right),y^{\prime }(t)=x(t)+\left(\{\begin{array}{cc}y(t)(x(t{)}^2+y(t{)}^2-1)\sin \left(\frac{1}{x(t{)}^2+y(t{)}^2}\right)& x(t{)}^2+y(t{)}^2\ne 1\\ 0& \mathit{otherwise}\end{array}\right)\}$$

$$\{(t^2+1)x^{\prime }(t)=-x(t)t+y(t),(t^2+1)y^{\prime }(t)=-x(t)-ty(t)\}$$

$$\{(x(t{)}^2+y(t{)}^2-t^2)x^{\prime }(t)=-2x(t)t,(x(t{)}^2+y(t{)}^2-t^2)y^{\prime }(t)=-2ty(t)\}$$

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

$$\{x(t)=t{x}^{\prime }(t)+f(x^{\prime }(t),y^{\prime }(t)),y(t)=t{y}^{\prime }(t)+g(x^{\prime }(t),y^{\prime }(t))\}$$

$$\{x^{\prime \prime }(t)=a{\mathrm{e}}^{2x(t)}-{\mathrm{e}}^{-x(t)}+{\mathrm{e}}^{-2x(t)}({\cos }^2(y(t))),y^{\prime \prime }(t)={\mathrm{e}}^{-2x(t)}\sin (y(t))\cos (y(t))-\frac{\sin (y(t))}{\cos {(y(t))}^3}\}$$

$$\{x^{\prime \prime }(t)=\frac{kx(t)}{{(x(t{)}^2+y(t{)}^2)}^{\frac{3}{2}}},y^{\prime \prime }(t)=\frac{ky(t)}{{(x(t{)}^2+y(t{)}^2)}^{\frac{3}{2}}}\}$$

$$\{x^{\prime \prime }(t)=-\frac{C(y(t))f\left(\sqrt{y^{\prime }(t{)}^2}\right)x^{\prime }(t)}{\sqrt{x^{\prime }(t{)}^2+y^{\prime }(t{)}^2}},y^{\prime \prime }(t)=-\frac{C(y(t))f\left(\sqrt{y^{\prime }(t{)}^2}\right)y^{\prime }(t)}{\sqrt{x^{\prime }(t{)}^2+y^{\prime }(t{)}^2}}-g\}$$

$$\{x^{\prime }(t)=y(t)-z(t),y^{\prime }(t)=x(t{)}^2+y(t),z^{\prime }(t)=x(t{)}^2+z(t)\}$$

$$\{a{x}^{\prime }(t)=(-c+b)y(t)z(t),b{y}^{\prime }(t)=(c-a)z(t)x(t),c{z}^{\prime }(t)=(a-b)x(t)y(t)\}$$

$$\{x^{\prime }(t)=x(t)(y(t)-z(t)),y^{\prime }(t)=y(t)(z(t)-x(t)),z^{\prime }(t)=z(t)(x(t)-y(t))\}$$

$$\{x^{\prime }(t)+y^{\prime }(t)=x(t)y(t),x^{\prime }(t)+z^{\prime }(t)=x(t)z(t),y^{\prime }(t)+z^{\prime }(t)=y(t)z(t)\}$$

$$\{x^{\prime }(t)=\frac{x(t{)}^2}{2}-\frac{y(t)}{24},y^{\prime }(t)=2x(t)y(t)-3z(t),z^{\prime }(t)=3x(t)z(t)-\frac{y(t{)}^2}{6}\}$$

$$\{x^{\prime }(t)=x(t)(y(t{)}^2-z(t{)}^2),y^{\prime }(t)=y(t)(z(t{)}^2-x(t{)}^2),z^{\prime }(t)=z(t)(x(t{)}^2-y(t{)}^2)\}$$

$$\{x^{\prime }(t)=x(t)(y(t{)}^2-z(t{)}^2),y^{\prime }(t)=-y(t)(z(t{)}^2+x(t{)}^2),z^{\prime }(t)=z(t)(x(t{)}^2+y(t{)}^2)\}$$

$$\{x^{\prime }(t)=-x(t)y(t{)}^2+x(t)+y(t),y^{\prime }(t)=x(t{)}^{2}y(t)-x(t)-y(t),z^{\prime }(t)=y(t{)}^2-x(t{)}^2\}$$

$$\{(x(t)-y(t))(x(t)-z(t))x^{\prime }(t)=f(t),(y(t)-x(t))(y(t)-z(t))y^{\prime }(t)=f(t),(z(t)-x(t))(z(t)-y(t))z^{\prime }(t)=f(t)\}$$

$$\{x_1^{\prime }(t)\sin (x_2(t))=x_4(t)\sin (x_3(t))+x_5(t)\cos (x_3(t)),x_3^{\prime }(t)+x_1^{\prime }(t)\cos (x_2(t))=a,x_4^{\prime }(t)-(1-\lambda )a{x}_5(t)=-m\sin (x_2(t))\cos (x_3(t)),x_5^{\prime }(t)+(1-\lambda )a{x}_4(t)=m\sin (x_2(t))\sin (x_3(t)),x_2^{\prime }(t)=x_4(t)\cos (x_3(t))-x_5(t)\sin (x_3(t))\}$$

$$y^{\prime }=f(x)$$

$$y^{\prime }=f(y)$$

$$y^{\prime }=f(x)g(y)$$

$$g(x)y^{\prime }=f_1(x)y+f_0(x)$$

$$g(x)y^{\prime }=f_1(x)y+f_n(x)y^n$$

$$y^{\prime }=f\left(\frac{y}{x}\right)$$

$$y^{\prime }=a{y}^2+bx+c$$

$$y^{\prime }=y^2-a^2{x}^2+3a$$

$$y^{\prime }=y^2+a^2{x}^2+bx+c$$

$$y^{\prime }=a{y}^2+b{x}^n$$

$$y^{\prime }=y^2+an{x}^{n-1}-a^2{x}^{2n}$$

$$y^{\prime }=a{y}^2+b{x}^{2n}+c{x}^{n-1}$$

$$y^{\prime }=a{x}^n{y}^2+b{x}^{-n-2}$$

$$y^{\prime }=a{x}^n{y}^2+b{x}^m$$

$$y^{\prime }=y^2+k{(ax+b)}^n{(cx+d)}^{-n-4}$$

$$y^{\prime }=a{x}^n{y}^2+bm{x}^{m-1}-a{b}^2{x}^{n+2m}$$

$$y^{\prime }=(a{x}^{2n}+b{x}^{n-1})y^2+c$$

$$(a_{2}x+b_2)(y^{\prime }+\lambda y^2)+a_{0}x+b_0=0$$

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