1. 
Open ode.m and ode_def.m Matlab functions and study how a simple ODE can be 
solved in Matlab. Try different types of commented ODE's, and check their solutions
for different initial values and integration time.
Write your own solution in Matlab for the following ODE: y' = -2*t*y^3 + t^3.
Characterize the type of ODE, plot the solution and analyse the stability.
2.
Test the ODE system defined in harm_osc.m. 
Try to find the physical interpretation of the solution and give a short description.
Explain the difference in solution obtained using different tolerances.
3.
Solve the system y1'=by1-cy1y2, y2'=-dy2+cy1y2 due to Lotka_Volterra, that describe
the coexistence of two populations. Plot the solution for b=1; c=1; d=10. 
Try to find nonzero population where one of populations disappear.
4.
Study the Matlab help for ode45. Using ode45, how you recognize that an ODE is stiff?
Which function will be probably better solution for a stiff ODE. 
5.
Use Huen's method - second-order Runge Kutta to solve ODE y'=-2*t*y^2 + t^3. 
Initial value, time step and duration of iteration are input parameters. 
Plot solution y(t) and compare your solution with the Matlab solution obtained in 1.
6.
Use Huen's method - second-order Runge Kutta to solve stiff ODE 
y'= -100*y+100*t+101. Initial value (should be close to 1), 
time step and duration of iteration are input parameters. Plot solution y(t)
and compare your solution with the Matlab solution obtained in 1.


Pack your solutions in a zip file and save it on the directory:
/home/scicomp/trobec/labs due to Wednesday 24:00.