Page 165 - Schaum's Outline of Differential Equations

CHAPTER 17

Reduction of Linear

Differential Equations

to a System of First-

Order Equations

AN EXAMPLE

In Chapter 15. we introduced Ihe idea ol 'a matrix wtlh associated concepts. Consider the following second-
order differential equation:

We see that (!7.l) implies

Since lhal dcrhalivcs can be expressed in man> ways- using primes or dots are but two of ihem -we let

• Then Kq. (17.1) can be written as the following matrix equation:

because because We note, final h, thai Eq. (17.1) can also be expr

Note that if .v(0) = 5 and *(()) = - 1 2 in (77.7). then these initial conditions are written as.c(0) = 5, v(0) = -!2.

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