solving nonlinear diffrential equation using ode45

I have never met this kind of non-linear equation, and this is my current code

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function homework1 = main1(t,X)

global m c k1 k3

A = [ -c/m -k1/m; 1 0 ] ;

f = 0.*((t>=0)-(t>=10))+ (3*cos(t^2)).*((t>10)-(t>=30))+(-10).*((t>30)-(t>=50));

F=[f/m;0];

C=X*[0 0;1 0] ;

B=C.^3;

homework1= [X(2);A*X-k3/m*B+F] ;

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clear all

close all

global m c k1 k3

m = 1; c = 0.02 ; k1 = 1.25; k3=0.05;

tspan= 0:0.1: 50 ;

X0 = [ -3, 5 ] ;

[ t X ] = ode45(@main1, tspan, X0);

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what I am specially struggling with is the

1. 'x^3' term, I can't express the appropriate term
2. plotting (x,t) as the 't' goes on
3. using ode45 is required

please help me...

Answer 1

[Ameer Hamza]

First, no need to use global variables. Using them is not a recommended practice. Second, just write your ODE inside the main1.

Write this in a script file

tspan= 0:0.1:50 ;
X0 = [5, -3] ;
[t, X] = ode45(@main1, tspan, X0);
plot(t,X)

And save the following function in the file "main1.m"

function homework1 = main1(t,X)
m = 1; 
c = 0.02;
k1 = 1.25;
k3=0.05;

if t < 10
    F = 0;
elseif t < 30
    F = 3*cos(t.^2);
else
    F = -10;
end

homework1= [X(2); -c/m*X(2)-k1/m*X(1)-k3/m*X(1).^3+F/m] ;
end

[alsgud qor]

um,so U r saying that to write them entirely to...User function 'main1.m'?or code tab?

sorry I m not a native speaker so I might got misunderstood

[Ameer Hamza]

Both are correct. But for most common use, follow the method In my updated answer.

[alsgud qor]

Thank U so much! so this might be the result right? I add some more thing to be more visible.

Just one more question please...because of the COVID-19, I have difficulty on my study....

and the thing U solved also required main1.m and sub1.m ....what could be the sub1.m? I think there is no need to use more than one function...?

[Ameer Hamza]

Yes, the output looks correct.

No, sub1.m is not required. You just need one function.

[alsgud qor]

thank U.the thing I just uploaded,Is it have the same process that u just code?

[Ameer Hamza]

alsgud, for your second file, the differential equation will be different. You first have to find the differential equation and then apply the code.

[alsgud qor]

thank U.I'll try and ask if I face difficulty directly