PLEASE USE MATLAB:

Using an autonomous first order differential equation to model the growth of biological samples.

dy/dt = y(1-y/3),y(0)=1

Obtain a solution to this DE using (a) Eulers method using t=0.5, (b) Eulers method using t=0.2, (c) ODE 45 with t=0.2 and (d) the analytical solution which is given as

y(t)= 3 - (6/(exp(t)+2))

Estimate the mean square error (MSE) in each numerical case. Use a time window from t=0 to t=10.

1. Plot the Eulers 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.

ENGR 232 MATLAB Assignment Week # 2 Using an autonomous first order differential equation to model the growth of biological samples. 4-0-1 dy 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 exp (t)+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 2. Use Matlab to get the EQUILIBRIUM value and determine the time instant 3. Find how long does it take the growth to double from 1.0 to 2.0? plot, annotated. The MSE values must also be displayed. when it is reached Provide answers to part (2) and (3) as comments or display them on the plot