[x,y]=dsolve('Dx=x-y-x*(x^2+y^2)','Dy=x+y-y*(x^2+y^2)','x(0)=2','y(0)=1')

　　得到的结果是解析解没有找到.

　　用数值解.

　　在Matlab下输入：edit,然后将下面两行百分号之间的内容,复制进去,保存

　　%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

　　functiony=zhidao_rk4_5(t,x)

　　%x,y变量分别用x(1),x(2)表示

　　y=[x(1)-x(2)-x(1)*(x(1)^2+x(2)^2);x(1)+x(2)-x(2)*(x(1)^2+x(2)^2)];

　　%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

　　在Matlab下面输入：

　　t_end=10;

　　x0=[2;1];

　　[t,x]=ode45('zhidao_rk4_5',[0,t_end],x0);

　　plot(t,x);

　　legend('x','y');

　　xlabel('t');

　　figure;

　　plot(x(:,1),x(:,2));

　　xlabel('x');

　　ylabel('y');