### Recent Question/Assignment

You can write the submission in word or using latex and export it as a file. You can take a screenshot of the codes you modify and enter in the file and everything should be a single file document.
Explain what the program below performs line by line:

Given system of differential equations:

Set up the system in matrix form (x´=Ax there x= ).
Sketch the direction vector for the solution curve at the point (-2, 1).
Determine eigenvalues and eigenvectors of A
Solve the system given x(0)=0,y(0)=10 (the solution curve passes the point
(0,10) at t = 0).
Solve the differential equation system:

Write briefly what the following program performs and adapt the program by writing appropriate syntax / mathematical expressions or numbers to sketch the solution curve in part c)

Given the 2nd order differential equation
mx’’+ ax’ + kx = cos x
there m = 1[kg],a = 0.4 [kg/s],k = 0.5 [kg/s^2 ],x(0) = 2,x’ (0) = 1.5.

Write about the given differential equation of a differential equation system. (Hint: Let ’= y). Then customize the code below to this system as must outline the solution curve of the system over the interval [0,6].