ABSTRACT
At the end of this chapter, you should be able to:
• identify and solve the auxiliary equation of a second-order differential equation
• solve a second-order differential equation of the form a d2y dx2
+ bdy dx
+ cy = 0
An equation of the form a d2y dx2
+ bdy dx
+cy=0, where a, b and c are constants, is called a linear secondorder differential equation with constant coefficients. When the right-hand side of the differential equation is zero, it is referred to as a homogeneous differential equation. When the right-hand side is not
equal to zero (as in Chapter 82) it is referred to as a non-homogeneous differential equation. There are numerous engineering examples of secondorder differential equations. Three examples are:
(i) L d 2q dt2
+ R dq dt
+ 1 C
q=0, representing an equation for charge q in an electrical circuit containing resistance R, inductance L and capacitance C in series.
