# ODE Solver with array value parameter

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Teo Protoulis on 20 Oct 2019
Commented: Dihan Zou on 11 Apr 2020
I need to solve the following differential equations:
where x1 and x2 are the states of the system and y is the input of the system and it is represented by a 1002x1 vector. How is it possible to solve this system of differential equations?
Star Strider on 21 Oct 2019
What you describe is not the correct approach, in part because MATLAB uses adaptive ODE solvers, not fixed-step ODE solvers.
See my Answer for the correct approach.

Star Strider on 21 Oct 2019
Try this example:
yv = randn(1002,1); % Create ‘y’
tv = 0:numel(yv)-1; % Create Corresponding Time Vector
Eqns = @(t,x,tv,yv) [x(2)-interp1(tv(:), yv(:), t); -3*x(2)-2*x(1)+3*interp1(tv(:), yv(:), t)];
tspan = linspace(0, 10, 50);
ic = [0; 1]; % Use The Correct Initial Conditions
[T, X] = ode45(@(t,x)Eqns(t,x,tv,yv), tspan, ic);
figure
plot(T, X)
grid
Provide your own vectors for ‘y’ (that I call ‘yv’ here) and the time vector (‘tv’ here) that corresponds to it.
Make other appropriate changes to reflect the actual values you intend to use.
Dihan Zou on 11 Apr 2020
Amazingly talented method. Thank you both!!!

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