MATLAB: How can i make the initial value variable? this is the first problem. in the code, i used ‘inline’ to assign values to variable (t). However, the equation which is in the inline function was copied manualy. is it possible to do it automatically

assign values to variablesinline()

clear all
  clc
  syms t y
    y=dsolve('Dy-y=t^2','y(0)=1');  
    simplify(y)                    
    y1=inline('3*exp(t) - 2*t - t^2 - 2','t')  
    t=-4;
    sayici=0;
    for i=1:7
        t=t+1;
        sayici=sayici+1;
        b(sayici)=y1(t);
    end
    b
    ezplot(y1,[-3 3])
    xlabel('t [-3 3]');
    ylabel('y');
    grid on

Best Answer

To make it a variable, declare it as such in your dsolve statement, then to use it as a variable, use matlabFunction and the plot function:
syms t y
y=dsolve('Dy-y=t^2','y(0)=y0');  
simplify(y)
fy = matlabFunction(y)          % Create Anonymous Function From ‘y’
t = linspace(-3, 3, 35);        % Vector: ‘t’
y0 = 0:5;                       % Vector: ‘y0’
[T,Y0] = ndgrid(t,y0);          % Create Grid Matrices
Y = fy(T,Y0);                   % Evaluate Function
figure(1)
plot(t, Y)
grid
legstr = strsplit(sprintf('y_0 = %.0f\n', y0), '\n');
legend(legstr(1:end-1), 'Location','NW')
The matlabFunction result is:
fy = @(t,y0)t.*-2.0+exp(t).*(y0+2.0)-t.^2-2.0
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