Page 171 - Schaum's Outline of Differential Equations

154 REDUCTION OF LINEAR DIFFERENTIAL EQUATIONS [CHAP. 17

17.7. Put the following system into the form of System (17.7):

Since this system contains a third-order differential equation in x and a second-order differential equation in y,
we will need three new x-variables and two new y-variables. Generalizing Step 2, we define

Thus,

or

These equations are equivalent to the matrix equation x(t) = A.(t)x(t) + f(t) if we define

Furthermore, if we define c = and = 1, then the initial condition can be given by x(t 0) = c.
t 0

17.8. Put the following system into the form of System (17.7):

Since the system contains a second-order differential equation in x and a first-order differential equation in y,