
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....
$\displaystyle 4x^{2}y''+4xy'+(4x^{2}25)y$
i do remember getting it into form by dividing each term by $\displaystyle x^{2}$
so now the equation will look like this...
$\displaystyle y''+(\frac{1}{x})y'+(1\frac{25}{4x^{2}})y=0$
ok so $\displaystyle n^{2}=\frac{25}{4}$
so the solution is:
$\displaystyle y=c_{1}J_{\frac{5}{2}}(x)+c_{2}J_{\frac{5}{2}}(x)$
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.