how to implement without using "function-end" command?

I'll start with an example. All the codes are from this website, http://12000.org/my_notes/matlab_ODE/

I'm trying to figure out how to use ode45

function first_oder_ode

t=0:0.001:5;   % time scalex
initial_x=0;

[t,x]=ode45( @rhs, t, initial_x);

plot(t,x);
xlabel('t'); ylabel('x');

      function dxdt=rhs(t,x)
          dxdt = 3*exp(-t);
      end
  end

Now I want to avoid using

function
end

Because I wanna see what's inside the function in the work space.

then I can simply write like

f=@(t,x)3*exp(-t)+x;        %%%define first order ode

t=0:0.001:5;                %%%time scalex
x_initial=0;                %%%x initial condition
[t,x]=ode45(f,t,x_initial); %%%solving ODE

plot(t,x);

This is easy one for getting numerical solution for 1st order ODE

The problem is, applying this into ODE system.

The Matlab code is (it's already in the website)

function second_oder_ode

% SOLVE  d2x/dt2+5 dx/dt - 4 x = sin(10 t)
% initial conditions: x(0) = 0, x'(0)=0

t=0:0.001:3;   % time scale

initial_x    = 0;
initial_dxdt = 0;

[t,x]=ode45( @rhs, t, [initial_x initial_dxdt] );

plot(t,x(:,1));
xlabel('t'); ylabel('x');

      function dxdt=rhs(t,x)
          dxdt_1 = x(2);
          dxdt_2 = -5*x(2) + 4*x(1) + sin(10*t);

          dxdt=[dxdt_1; dxdt_2];
      end
  end

How do I write this in another way without using "function - end"? is it possible?

[Steven Lord]

Rather than making the outer function into a script, I recommend giving it some output arguments. This way you don't clutter the caller's workspace with temporary variables that are only needed to help the code compute the variables in which you're interested.

Answer 1

[Walter Roberson]

rhs = @(t, x) [x(2); -5*x(2) + 4*x(1) + sin(10*t)];

[Hoon]

so, I wrote like this

t=0:0.001:3;   % time scale
initial_x    = 0;
initial_dxdt = 0;
rhs = @(t, x) [x(2); -5*x(2) + 4*x(1) + sin(10*t)];
[t,x]=ode45( @rhs, t, [initial_x initial_dxdt] );
plot(t,x(:,1));
xlabel('t'); ylabel('x');

It doesn't work

[Hoon]

OH!!! it works!!! I have to loose @!