Consider a system of coupled ordinary differential equations (ODEs) representing a set of chemical reactions: dx/dt= -0.1x

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Question:

Consider a system of coupled ordinary differential equations (ODEs) representing a set of chemical reactions:

dx/dt= -0.1x + 0.02y
dy/dt= 0.1x - 0.02y - 0.05z
dz/dt= 0.05y - 0.1z

Write a MATLAB script that numerically solves this system of ODEs using the ode45 solver. Set the initial conditions as (x(0) = 1), (y(0) = 0), and (z(0) = 0). Integrate the system over the time interval [0, 10] with a variable time step.

A. Solving the ODEs, plot the solutions (x(t)), (y(t)), and (z(t)) on the exact figure. Calculate and plot the total concentration (x + y + z) over time.

B. compute and display the maximum concentration reached for each species and the corresponding time. Provide comments in your code explaining each major step.