Write the following second order homogeneous differential equation as a system of first-order
−3y” − 5y’ + 2y = 0
Find the general solution to your system of first order differential equations determined in
part 1 above.
Hence write down the general solution to the original differential equation in part 1.
For both of the following systems of differential equations:
Find the real general solution.
Determine the critical point.
Determine the type of the critical point.
Determine the stability of the critical point.
y1′ = 7y1 − 2y2
y2′ = 4y1 + 3y2
y1′ = 8y1 − ?y2
y2′ = y1 + 10y2
Find the location, type and stability of all critical points by linearization of the following
nonlinear homogeneous system of differential equations.
y1′ = y2 − y22
y2′ = y1 − y12
Find the general solution for the following linear non-homogeneous system of differential
y1′ = 4y1 − 8y2+ 2 cosh(t)
y2′ = 2y1− 6y2 + cosh(t) + 2 sinh(t)