Using an autonomous first order differential equation to model the growth of bio

Question

Using an autonomous first order differential equation to model the growth of biological samples dy , y dt Obtain a solution to this DE using (a) Euler's method using At-0.5, (b) Euler's method using At-0.2, (c) ODE 45 with At-0.2 and (d) the analytical solution which is given as 6 yCexp()+2 Estimate the mean square error (MSE) in each numerical case. Use a time window from t=0 to t=10. 1. Plot the Euler's solutions, ODE solution and analytical solution on a single plot, annotated. The MSE values must also be displayed. 2. Use Matlab to get the EQUILIBRIUM value and determine the time instant when it is reached. 3. Find how long does it take the growth to double from 1.0 to 2.0? Provide answers to part (2) and (3) as comments or display them on the plot.

Explanation / Answer

Similarly for delta t= 0.2 take n= 50. Rest all the values will be the same.

Further to solve using ode45:

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