# MATLAB MATLAB - solving equation with Bessel function

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1. Jan 1, 2019

### kravky

Hello,

i am trying to solve this equation for x

besselj(0,0.5*x)*bessely(0,4.5*x)-besselj(0,4.5*x)*bessely(0,0.5*x) ==0;

I tried vpasolve, but it gave me answer x=0 only. fzero function didnt work, too.
What function can solve this equation?

Thanks

2. Jan 1, 2019

### Orodruin

Staff Emeritus
Please show us exactly the code you have tried. Otherwise it is impossible to tell where you might have gone wrong. fzero works perfectly fine for me.

3. Jan 1, 2019

### kravky

Yes. I misused fzero function. now it works for me aswell!

Code (Text):
function ffu = f(x)
ffu = besselj(0,0.5*x)*bessely(0,4.5*x) - besselj(0,4.5*x)*bessely(0,0.5*x);
and fzero
Code (Text):
fun=@f
x0=2;
S=fzero(fun,x0)

will find solution. It finds only one solution which is close to the x0 value but its not the problem.

4. Jan 1, 2019

### Orodruin

Staff Emeritus
Yes, fzero finds just one solution. It will find different solutions depending on your x0 input.

Also, when you have such a short and simple function, you can just as well define an inline function instead of writing an entire function file.

5. Jan 1, 2019

### kravky

I understand. A good way is to use ezplot as well for a rough estimation of points, where functions is zero (intersection with x axis) and then use this rough guess as x0 input in fzero for precise value