how can i make the initial value variable? this is the first problem. in my 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?

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

[Star Strider]

Essential duplicate of: http://www.mathworks.com/matlabcentral/answers/220284-i-aimed-to-solve-a-differantial-equation-with-an-initial-value-but-how-can-i-make-the-initial-value

[hamit Kenan]

it was deleted.

Answer 1

[Star Strider]

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