**Question 1**

**Part 1**

Write the following second order homogeneous differential equation as a system of first-order

differential equations.

−3y” − 5y’ + 2y = 0

**Part 2**

Find the general solution to your system of first order differential equations determined in

part 1 above.

**Part 3**

Hence write down the general solution to the original differential equation in part 1.

.

**Question 2**

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.

**Part 1 **

y1′ = 7y1 − 2y2

y2′ = 4y1 + 3y2

**Part 2**

y1′ = 8y1 − ?y2

y2′ = y1 + 10y2

**Question 3 **

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

**Question 4 **

Find the general solution for the following linear non-homogeneous system of differential

equations.

y1′ = 4y1 − 8y2+ 2 cosh(t)

y2′ = 2y1− 6y2 + cosh(t) + 2 sinh(t)

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