# Bessel's equation

• Apr 10th 2011, 12:38 PM
slapmaxwell1
Bessel's equation
ok im supposed to find the general solution of the differential equation on

im a little, well a lot stuck on this problem....

$4x^{2}y''+4xy'+(4x^{2}-25)y$

i do remember getting it into form by dividing each term by $x^{2}$

so now the equation will look like this...

$y''+(\frac{1}{x})y'+(1-\frac{25}{4x^{2}})y=0$

ok so $n^{2}=\frac{25}{4}$

so the solution is:

$y=c_{1}J_{\frac{5}{2}}(x)+c_{2}J_{\frac{-5}{2}}(x)$

its not that straight forward is it? ok so let me know where im screwing up so i can try to fix it. thanks in advance.