Rewrite the following systems of differential equations as first order systems, written in the standard way (i.e. in the same form as in the previous two problems). To do that, you will need to introduce new unknowns and equations. You do not need to find the solution to the resulting first order systems. a) Rewrite the differential equation as a first order system: y'''-3y''+4y = 3cost b) Rewrite the system of differential equations as a first order system:  x1''+ 2x2' + 5x1'= e4t x2''+ 6x1 − x2 = e3t

Rewrite the following systems of differential equations as first order systems, written in the standard way (i.e. in the same form as in the previous two problems). To do that, you will need to introduce new unknowns and equations. You do not need to find the solution to the resulting first order systems.

a) Rewrite the differential equation as a first order system:

y'''-3y''+4y = 3cost

b) Rewrite the system of differential equations as a first order system: 

x₁''+ 2x₂' + 5x₁'= e^4t
x₂''+ 6x₁ − x₂ = e^3t