how can i get the values of y1, y2? i am only getting the graph.

function Shrinking_bvp4c
clc
clear all
clear all
% defining parameters
k=0.2,K=0.2,M=0.2,S=2;
sol1   = bvpinit(linspace(0,3,30),[1 0 1 0]);
    sol    = bvp4c(@bvp2D,@bc2D,sol1);
    x      = sol.x;
    y      = sol.y; 
    
    %%% Plotting of the velocity
    figure (1)
    plot(x, y(2, :) ,'linewidth', 1)
    hold on
    xlabel('\eta', 'fontweight', 'bold', 'fontsize', 16)
    ylabel('f^/(\eta)', 'fontweight', 'bold', 'fontsize', 16)
   
    %% Residual of the boundary conditions
  function residual = bc2D(y0, yinf)         
     residual=[y0(1)-S;  y0(2)+1; yinf(2); yinf(3)];      
  end

   %%  System of First Order ODEs
  function yvector = bvp2D(t,y)
        yy1 = 1/y(1)*(y(2)*y(2)-y(1)*y(3)-y(4)+k*(2*y(2)*y(4)-y(3)*y(3))+M*y(2)+K*y(2));
      yvector  = [y(2);y(3);y(4);yy1];
  end
end

Answer 1

[Stephen23]

Return them as function outputs:

https://www.mathworks.com/help/matlab/ref/function.html

https://www.mathworks.com/help/matlab/learn_matlab/calling-functions.html

[x,y] = Shrinking_bvp4c % here are the values

x = 1×33

0 0.1034 0.2586 0.4138 0.5690 0.7241 0.8793 1.0345 1.1897 1.3448 1.4483 1.5517 1.6552 1.7586 1.8103 1.8621 1.9138 1.9655 2.0172 2.0690 2.1207 2.1724 2.2241 2.2759 2.3276 2.3793 2.4310 2.4828 2.5862 2.6897

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

y = 4×33

2.0000 1.8989 1.7565 1.6258 1.5074 1.4016 1.3084 1.2276 1.1587 1.1012 1.0687 1.0406 1.0165 0.9963 0.9874 0.9794 0.9721 0.9656 0.9598 0.9546 0.9500 0.9459 0.9424 0.9394 0.9368 0.9346 0.9328 0.9313 0.9291 0.9278 -1.0000 -0.9542 -0.8807 -0.8030 -0.7226 -0.6412 -0.5603 -0.4816 -0.4065 -0.3361 -0.2924 -0.2516 -0.2137 -0.1790 -0.1629 -0.1476 -0.1331 -0.1194 -0.1066 -0.0945 -0.0833 -0.0728 -0.0632 -0.0543 -0.0462 -0.0388 -0.0321 -0.0261 -0.0162 -0.0088 0.4296 0.4562 0.4886 0.5112 0.5232 0.5247 0.5158 0.4972 0.4700 0.4354 0.4091 0.3807 0.3507 0.3197 0.3040 0.2881 0.2723 0.2564 0.2407 0.2250 0.2095 0.1942 0.1792 0.1644 0.1500 0.1359 0.1222 0.1088 0.0834 0.0597 0.2759 0.2389 0.1778 0.1119 0.0436 -0.0244 -0.0895 -0.1490 -0.2008 -0.2430 -0.2653 -0.2828 -0.2954 -0.3033 -0.3055 -0.3066 -0.3067 -0.3058 -0.3039 -0.3012 -0.2976 -0.2932 -0.2881 -0.2824 -0.2761 -0.2692 -0.2618 -0.2541 -0.2375 -0.2199

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

plot(x, y(2, :) ,'linewidth', 1)
hold on
xlabel('\eta', 'fontweight', 'bold', 'fontsize', 16)
ylabel('f^/(\eta)', 'fontweight', 'bold', 'fontsize', 16)

function [x,y] = Shrinking_bvp4c % <- define the output arguments here.

%!!!!!!!!!!! Do NOT put anti-pattern CLEAR at the top of a function !!!!!!!!!!

% defining parameters
k=0.2;
K=0.2;
M=0.2;
S=2;

sol1   = bvpinit(linspace(0,3,30),[1 0 1 0]);
sol    = bvp4c(@bvp2D,@bc2D,sol1);
x      = sol.x;
y      = sol.y; 

%% Residual of the boundary conditions
    function residual = bc2D(y0, yinf)         
        residual=[y0(1)-S;  y0(2)+1; yinf(2); yinf(3)];      
    end

%%  System of First Order ODEs
    function yvector = bvp2D(t,y)
        yy1 = 1/y(1)*(y(2)*y(2)-y(1)*y(3)-y(4)+k*(2*y(2)*y(4)-y(3)*y(3))+M*y(2)+K*y(2));
        yvector  = [y(2);y(3);y(4);yy1];
    end
end

[Saswati]

function [x,y]=Shrinking_bvp4c

if I put the above line , I am only getting the values of x. how to get values of y?

[Stephen23]

"if I put the above line , I am only getting the values of x. how to get values of y?"

I already showed you that in my answer (and also linked to the documentation which explains how).

Here it is again, you have to call your function with TWO output arguments (not ONE like you are doing):

[x,y] = Shrinking_bvp4c
%^^^ !!!! you need TWO output arguments when you call the function !!!!

Lots of MATLAB functions have multiple outputs, this is a very important basic MATLAB syntax.