ode45 is not generating the proper graph for this 1st order diff. eqn.

For this problem, I am given the equation:

Solving for it by hand, I found the answer to be x(t) = (3/5)*e^(5*t) - (3/5)

From this, I would expect the graph to be an exponential curve that horizontally asymptotes at -(3/5) and cross the origin at (0,0)

However, when I inputted this into MATLAB using ode45, I got a graph that horizontally asymptotes at the x-axis and does not cross through the origin.

Its very possible that I messed up in the code for ode45 but I'm not sure where it occured. Here is the code I used:

clear all

hw0p4func = @(t,x) (5*x)+3;

time = [0 10];

initial = [0 0];

[t,x] = ode45(hw0p4func, time, initial);

plot(t,x(:,1)),title('Problem 4: x vs. time'),xlabel('time'),ylabel('x'),

For reference, this is what the graph should look like:

I'd like to know what exactly I've done wrong with my code here.

Answer 1

[Piotr Balik]

It is working fine as far as I've tested it:

clear,close all,clc

hw0p4func = @(t,x) (5*x)+3;

initial = [0 0];
time = [0 10];
[t,x] = ode45(hw0p4func, time, initial);
plot(t,x(:,1))
hold on

time = [0 -1]; %backwards in time
[t,x] = ode45(hw0p4func, time, initial);

plot(t,x(:,1)),title('Problem 4: x vs. time'),xlabel('time'),ylabel('x'),
axis([-1 2 -1 10])

You just forgot to compute the negative time part. You can add analytical plot for comparison:

t = -1:0.1:1;
y=(3/5)*exp(5*t) - (3/5);
plot(t,y,'--')

[T. Senevirathne]

Oh wow, I never even thought about the time interval limiting my solution. Thank you!

Is it possible to do [-1 10] for the time interval or do you have to do [0 10] and [0 -1] and merge the graphs together?

[Piotr Balik]

It is possible, but since you provided initial condition at , I had to resort to going backward in time.

If you know , then you can use interval in straightforward fashion: time=[ -1 10]