How do I solve a linear state observer using only Matlab ODE45 and NO toolboxes nor Simulink?

I have attempted to simulate the observed states of a linear state observer.

Refer to the attached code below: I ultimately need to calculate Xhat, and by doing so I call the second ODE45. The anonymous function that ODE45 handles must make use of X in it's calculation (which is determined by the first call of ODE45). After calling the first ODE45 that calculates X, it returns a 3x50 matrix; 3 states over 50 time instances. But only that X at a specific time t, corresponding to the calculation of Xhat at that SAME time t, must be used.

i.e. find X at time t and then use that value to find Xhat at the same time t, and then do all that over the whole timespan [0 1].

I've tried using interp1 but could not get it working, perhaps my syntax was wrong.

CODE: --------

clear
clc

%%%%System matrices %%%
 A = [ 1 2 0
       3 4 1
       1 2 0];

    B = [1000 ; -1000 ; 0.1];

    C = [ 0  1  1 ];

    D = 0;
    u = 1;

    %%%Arbitrary observer matrices %%%

    Ahat = A;   % arbitrary values used just to test the ODE solver later on
    Bhat = B;   % same explanation as above
    Ke = [1;1;1]; % same as above
    Abar = Ahat - Ke*C;

%%%plotting the actual states  
x1_0 = 1;
x2_0 = 1;
x3_0 = 1;
X_0 = [x1_0;
       x2_0
       x3_0];

x1timespan = linspace(0,1,25); % Generate t for X
dxdt = @(t,x) [A(1,1)*x(1) + A(1,2)*x(2) + A(1,3)*x(3) + B(1,1)*1;
               A(2,1)*x(1) + A(2,2)*x(2) + A(2,3)*x(3) + B(2,1)*1;
               A(3,1)*x(1) + A(3,2)*x(2) + A(3,3)*x(3) + B(3,1)*1]

[tx,X] = ode45(dxdt, [0 1], [x1_0 x2_0 x3_0]); % Generates the solution to the linear system 

plot(tx,X)
title('Actual States')

%%Plotting the observed states
dxhatdt = @(t,Xhat) [Ahat*Xhat + Bhat*u + Ke*((C*X) - (C*Xhat))]

Xhat_0 = [0;0;0];
[txhat,Xhat] = ode45(dxhatdt, [0 1], Xhat_0)

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