Bessel's Equation
By John Campbell •
How can I solve this Bessel's Equation?
$$x^2*y''+x*y'+(x^2-v^2)y=0$$
First I did that:
$$y''+\frac{1}{x}y'+\frac{(x^2-v^2)}{x^2}y = 0$$
Then,
$$ce^{-\int\left[\frac{1}{x}\right]dx}=ce^{-\ln(x)}=-cx$$
$\endgroup$ 31 Answer
$\begingroup$$$x^2*y''+x*y'+(x^2-v^2)y=0$$ is the Bessel ODE which solutions are linear combinations of the Bessel functions of the first- and second- kind.
$\endgroup$
