Computing a differential equation using a bessel function.

How do we use the bessel function of :

y = besselj(0,x)

to compute the differntial equation of ?

[John D'Errico]

Please dont ask exactly the same question again, just to get yet more information. I closed your first question.

Answer 1

[Torsten]

The solution y of this differential equation is a combination of J_0(x) and Y_0(x), the Bessel function of the first and second kind of order 0.

So using it to solve the differential equation makes no sense.

syms x y(x)
eqn = diff(y,x,2)*x^2 + diff(y,x)*x + x^2*y == 0;
Dy = diff(y,x);
conds = [y(0)==1,Dy(0)==0];
sol = dsolve(eqn,conds);
hold on
fplot(sol,[0 100])
x = 0:0.1:100;
plot(x,besselj(0,x))
hold off

[Howie]

how would we graph this?

[Torsten]

"this" is what ?

[Howie]

sorry, how do we graph the answer to our equation?

[Torsten]

See above. You have to specify two initial conditions for the differential equation to get a unique solution. The conditions y(0) = 1 and y'(0) = 0 give J_0(x). As noted, other initial conditions will give a "mixture" of J0(x) and Y0(x).

[Howie]

How do we graph it in the way to look like this? Or the same format?

[Torsten]

Done.

But now it's enough about Bessel, isn't it ?

[Howie]

Yes thank you so much!