Question

First use (20) in Section 6.4.

y'' +

1 − 2a

x

y' +

b²c²x^{2c − 2} +

a2 − p2c2

x2

y = 0,    p ≥ 0    (20)

Express the general solution of the given differential equation in terms of Bessel functions. Then use (26) and (27)

J1/2(x)	=	2 πx sin(x)		(26)
J−1/2(x)	=	2 πx cos(x)		(27)

to express the general solution in terms of elementary functions. (The definitions of various Bessel functions are given here.)

y'' + y = 0

y(x) =

C1

x

sin(x) +

C2

x

cos(x)y(x) =

C1

x

sin(2x) +

C2

x

cos(2x)     y(x) =

C1

x

sin(x) +

C2

x

cos(x)

y(x) = C₁ sin(2x) + C₂ cos(2x)

y(x) = C₁ sin(x) + C₂ cos(x)

First use (20) in Section 6.4 a2 - p2c2 Express the general solution of the given differential equation in terms of Bessel functions. Then use (26) and (27) 2 x sin(x) (26) ไม่2(x) J-1/2(x) 1/-cos(x) (27) = to express the general solution in terms of elementary functions. (The definitions of various Bessel functions are given here.) o y(x)sin(x)cos(x) Xx o y(x)sin (2x) cos(2x) Xx o x)-C1 sin(2x) C2 cos(2x) o yx)-C1 sinx)C2 cos(x)

Answer 1

2C 一(2) 12 LC- . Sduthn LS