ODE Piecewise Linear Function Help

Not sure what's wrong but this is what I have to do:

The listing of a Matlab script file which uses dsolve() to solve the following ODE and plot the results from t=0 to t=3. dx/dt + 2 x = f(t) with x(0) = 1 and where

f(t) = exp(-t) 0 <= t <= ln(2) f(t) = 4 for ln(2) < t <=ln(3) f(t) = 0 otherwise

SHOW: The output generated by the script file The plot generated by the script file

THIS IS WHAT I HAVE..

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%last modified: 2/27/2014
%Matlab
%for piecewise continuous input
%of first order linear systems
clear all
clc
format compact
% Example
% dx/dt + 2x = f(t)
% f(t) = 1 for 0<=t<=1 and 0 otherwise
% Symbolic approach
% Find x in the first interval
% Note the use of pure symbolics instead
% of a character string solution like
% x1 = dsolve('Dx1+x1=1','x1(0)=0')
syms t x1(t)
dx1 = diff(x1);
t = 1;
x1 = dsolve(dx1+2*x1==exp(-t), x1(0)==1);
display(['x1 = ', char(vpa(x1,3))])
%Use solutions for first interval to find
%IC for second interval
x2_IC = subs(x1);
display(['x2_IC = ', char(vpa(x2_IC,3))])
%Find solution in second interval using
%x2_IC as an IC
syms t x2(t)
dx2 = diff(x2);
x2 = dsolve(dx2+2*x2==4, x2(log(2))==x2_IC);
x3_IC = subs(x2);
display(['x3_IC = ', char(vpa(x3_IC,3))])
syms x3(t)
dx3 = diff(x3);
x3 = dsolve(dx3+2*x3==0, x3(log(3))==x3_IC);
display(['x3 = ', char(vpa(x3,3))])
%Plot the results
t = 0:0.01:1;
xx1 = subs(x1);
plot(t,xx1,'linewidth', 3,'color','red')
t = 1:0.01:3;
xx2 = subs(x2);
plot(t,xx2,'linewidth',3,'color','green')
t = 3:0.01:5;
xx3 = subs(x3);
hold on
plot(t,xx3,'linewidth',3,'color','blue')
grid on
xlabel('t','FontSize',14)
ylabel('x','FontSize',14)
title('x vs time','FontSize',14)
hold off

[Mischa Kim]

Do you need to solve it using symbolic math (rather than doing it numerically)?

[Braulio Diaz]

Actually, either one is okay..

Answer 1

[Mischa Kim]

In this case have a look at:

function my_DE()

x0    = 1;
tspan = linspace(0,3,1000);
[T,X] = ode45(@DE, tspan, x0);

plot(T,X)
grid
end

function dX = DE(t,x)
dX = -2*x + f(t);
end

function fval = f(t)
if     (t <= log(2))
    fval = exp(-t);
elseif (t > log(2)) && (t <= log(3))
    fval = 4;
else
    fval = 0;
end
end

...not including the color coding in the plot.

[Braulio Diaz]

Nice! Thanks a lot Mischa!

[Braulio Diaz]

Mischa, how would I do this using symbolic math?