Consider the initial value problem:
y" - 5y' + 6y = -5sin(2t); y(0) = -5, y'(0) = 2
Write the differential equation above as a first-order system for the unknowns u, v, where u=y and v is defined as in the lecture notes. You do not need to solve the system.

Step-by-step explanation:

The given initial value problem is;

Let

Differentiating both sides of equation (1) with respect to , we obtain:

Differentiating both sides of equation (2) with respect to gives:

From equation (1),

Putting t=0 into equation (2) yields

Also putting t=0 into equation (3)

The system of first order equations is: