Solving a first-order ODE given an input vector

I am trying to solve the following ODE:

The purpose of this is to generate a timeseries y(t) given an input timeseries z(t) that I have already created. y(t) should be a vector of the same dimensions as z(t). However, I am not sure how to go about this using Matlab. I have tried using ode45 with the vector z(t) and the scalar k added as inputs:

odefun= @(t, y, z, h) z-h*y;

[~, y_sim]=ode45(@(t, y) odefun(t, y, z_sim, k), 1:20000, 0); %Set first value of y to zero

However, this returns the following error:

Error using odearguments (line 93)

@(T,Y)ODEFUN(T,Y, Z_SIM, K) must return a column vector.

How might I go about doing this?

[Pavitra Vaishali]

Hey were you able to find the solution. If so, please help me too I am facing similar problem. Only change is I have a matrix instead of single value at time.

Meaning for each time stamp I will get a matrix.

Answer 1

[Ameer Hamza]

This is actually equivalent to solving an ODE with time-varying term. See the example here: https://www.mathworks.com/help/matlab/ref/ode45.html#bu3l43b which deals exactly the same problem. You first need to define the value of z inside odefun as a function of t.