Consider dx/dy=2x+2y dy/dt=-4x+6y

a)Compute the eigenvalues

b)For each eigenvalue, compute the associated eigenvectors.

c)Using HPGSystemSolver, sketch the direction field for the system,and plot the straight-line solutions(if there are any). Plot the phase portrait.

d) For each eigenvalue, specify the corresponding straight-line solution(if there are any), plot its x(t) and y(t) graphs.

e)Find the general solution of the system.

f)Find the equilibrium points of the system.

g)Find the solution that satisfies the initial condition (x0, y0)=(1,1).

h)Is the origin a spiral source, spiral sink, or center.