MATLAB: How to implement without using “function-end” command

@functionode45

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?

Best Answer

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