Keep Getting This Error : @(T,X)SECO​ND_ORDER(T​,X,A0,A1) must return a column vector.

Hello all! I'm trying to solve the second order equation y'' + a1*y' + a0*y = 0 using ode45 and I've gotten stuck and keep getting the same error. My current code:

 %%Behavior of second order ODEs
 % y'' + a1*y' + a0*y = 0 
 % x' = Ax
 N=1000;
 T=10;
 t = linspace(0,T,N); % initialize the time vector
 a0=0;
 a1=0;
 x0=2; %y
 x1=0; %dy
 x=[x0;x1];
 dy = second_order(t,x,a0,a1);
 %ODE
 [t,x] = ode45(@(t,x)second_order(t,x,a0,a1),t,x0);
 plot(t,x,'k-','LineWidth',2);

My Function:

 function [ dx ] = second_order(t,x,a0,a1 )
  A=[0,1;-a0,-a1];
  dx= A*x;
 end

Answer 1

[James Tursa]

This line declares initial state that you pass to ode45 to be a scalar:

x0=2; %y

So when you call ode45 with x0 it assumes the state is a scalar. But you have this line also:

x=[x0;x1];

This 2-element vector is what you need to pass to ode45 as the initial state:

[t,x] = ode45(@(t,x)second_order(t,x,a0,a1),t,x);

[Jenna Brannon]

Wow, I have been looking at this too long. Thank you!