How to write ode45 function correctly

I am trying to solve 2nd order ODE using matlab and I am having a problem with my function file.

My original equation is as follows:

I wrote my 2nd order in terms of 1st order and have 2 sets of equation as the following:

x1=x

x2=dx

And my 1st order ode’s are:

dx=x2

dxdt=b1*x1-a*x2+b2*x1^4+4t

The function I wrote in matlab is:

function dxdt= model(t,x,m,a,b1,b2)

x=x(1);

dx=x(2);

dxdt(1)=dx;

dxdt(2)=b1*x-a*dx+b2*x^4+4*t;

end

But matlab kept saying there is an error at x=x(1). I know x1 and x2 are vectors but I am not sure how to write it in this function.

Answer 1

[Ameer Hamza]

You are oberwriting variable 'x' inside model(). Try this

m = 1;
a = 0.5;
b1 = 0.1;
b2 = 0.2;

tspan = [0 10];
ic = [1; 0];

ode45(@(t,x) model(t,x,m,a,b1,b2), tspan, ic)

function dxdt= model(t,x,m,a,b1,b2)
x_=x(1);
dx=x(2);
dxdt(1)=dx;
dxdt(2)=b1*x_-a*dx+b2*x_^4+4*t;
dxdt = dxdt(:); % it must return a column matrix
end