Фазовые портреты «на пальцах» или что можно узнать о решениях диффура, не решая его

clear all; close all; clc

f = @(t,Y) [Y(1)+Y(2); 4*Y(1)-2*Y(2)];

y1 = linspace(-2,2,20);
y2 = linspace(-2,2,20);

% creates two matrices one for all the x-values on the grid, and one for
% all the y-values on the grid. Note that x and y are matrices of the same
% size and shape, in this case 20 rows and 20 columns
[x,y] = meshgrid(y1,y2);

u = zeros(size(x));
v = zeros(size(x));

% we can use a single loop over each element to compute the derivatives at
% each point (y1, y2)
t=0; % we want the derivatives at each point at t=0, i.e. the starting time
for i = 1:numel(x)
    Yprime = f(t,[x(i); y(i)]);
    u(i) = Yprime(1);
    v(i) = Yprime(2);
end

quiver(x,y,u,v,'r'); figure(gcf)
xlabel('y_1')
ylabel('y_2')
axis tight equal;