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

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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.

Accepted Answer

Piotr Balik
Piotr Balik on 2 Sep 2021
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,'--')
  2 Comments
Piotr Balik
Piotr Balik on 3 Sep 2021
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]

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