# MATLAB: Merge three initial values ​​into one code by runge-kutta

plot

h=0.5;                                             % step sizex = 0:h:100;                                         % Calculates upto y(3)Y = zeros(1,length(x)); %y(1) = [0.2;0.3;0.2];y(1) = 0.2; % redo with other choices here.     % initial conditionF_xy = @(t,r) 3.*exp(-t)-0.4*r;                    % change the function as you desirefor i=1:(length(x)-1)                              % calculation loop    k_1 = F_xy(x(i),y(i));    k_2 = F_xy(x(i)+0.5*h,y(i)+0.5*h*k_1);    k_3 = F_xy((x(i)+0.5*h),(y(i)+0.5*h*k_2));    k_4 = F_xy((x(i)+h),(y(i)+k_3*h));    y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h;  % main equation  end% validate using a decent ODE integrator  tspan = [0,100]; y0 = -0.5;[tx, yx] = ode45(F_xy, tspan, y0)plot(x,y,'o-', tx, yx, '--')
how can i run this code for three initial value and plot it in same graph?

• h=0.5;                                             % step sizex = 0:h:100;                                         % Calculates upto y(3)ibc = [0.2;0.3;0.2];Y = zeros(length(ibc),length(x));for j = 1:length(ibc)    y = zeros(1,length(x)) ;    y(1) = ibc(j) ;    % redo with other choices here.    % initial condition    F_xy = @(t,r) 3.*exp(-t)-0.4*r;                    % change the function as you desire    for i=1:(length(x)-1)                              % calculation loop        k_1 = F_xy(x(i),y(i));        k_2 = F_xy(x(i)+0.5*h,y(i)+0.5*h*k_1);        k_3 = F_xy((x(i)+0.5*h),(y(i)+0.5*h*k_2));        k_4 = F_xy((x(i)+h),(y(i)+k_3*h));        y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h;  % main equation            end    Y(j,:) = y ;        % validate using a decent ODE integrator    tspan = [0,100]; y0 = -0.5;    [tx, yx] = ode45(F_xy, tspan, y0) ;     plot(x,y,'o-', tx, yx, '--')    hold onend