Page 100 - Schaum's Outline of Differential Equations

CHAPTER 9

Second-Order

Linear Homogeneous

Differential

Equations with

Constant Coefficients

JOTROftUCTORY REMARK
..• .,*flwsjfatj»*e have concentrated on first-order differential equations. We will now turn our attention to the
§ee(Jjfd:~Gidet .case. After investigating solution techniques, we will discuss applications of these differential
aeq«atiQa$"(se? Chapter 14).

;THl/GSARACTERISTIC EQUATION
-. • ", CSrrespottSng to the differential equation

jji'whieli'tfj. afld a 0 are constants, is the algebraic equation

1
2
'tt'Meli is obiajjifefl, from Eq. (9.1) by replacing y", y' and y by A , A, , and A° = 1, respectively. Equation (9.2) is
•ealle4 ^ft 'chofdtteristic equation of (9.1).
2
Example 9-1'' * The characteristic equation of y" + 3y' — 4y = 0 is X + 3X - 4 = 0; the characteristic equation of

83
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