Page 563 - Modelling in Transport Phenomena A Conceptual Approach

B.2. SECOND-ORDER LINEAR DIF'FERENTlAL EQUATIONS 543

1-P
'=,-p+j
- 1+3
-
2+3-3=2 (3)

Note that a > 0 and R is calculated from Eq. (B.2-22) as

Since n is an integer, the solution is given in the form of Eq. (B.2-21)

Y = x2 [ClJ2(4 + C2Y2(2)] (6)

b) The equation can be rearranged in the fonn

Therefore, p = 0; a = - 1; j = 2; b = 0. Since b = 0, the equation is reducible to
Bessel's equation. The terms a, p, and n are calculated from Eqs. (B.2-17)-(B.2-
19) as
2-p+j
CY=
L
- 2-0+2 =2
-
2

1-P
'=2-p+j
1
- 1-0 -_ (9)
-
2-0+2-4
,/( 1 - p)2 - 4b
n=
2-p+j
1
- d(1 - 0)2 - (4)(0) =-
-
2-0+2 4