Showing that bessel function satifies differential equation

[1Kris]

Homework Statement

Show that y'' + ((1+2n)/x)y' + y = 0 is satisfied by x^-nJ_n(x)

Homework Equations

y= x^-nJ_n(x)
y'=-x^-nJ_n+1(x)
y''=nx^-n-1J_n+1(x) - x^-n(dJ_n+1(x)
/dx)

The Attempt at a Solution

Equation in question becomes:
x^-n(2(n/x)J_n+1 - J_n - ((1+2n)/x)J_n+1 + J_n)

= x^-n(-x^-1J_n+1)
which isn't 0 ?

Perhaps I made the mistake when I differentiated y?
Help would be very much appreciated.

 

[masqau]

Well, when u are going differentiation, Y=X*J(x)
You see its a product of X and J(X), so u have to used product rules.
Y'=J(x)D(x)+xD(J(x)).