> From: Radovan Omorjan
> Hello,
>
> I looked at the Maxima archive and did not find this (if I am
> wrong, sorry)
>
> The Bessels' equation will solve with ode2
>
> ode2(x2*'diff(y,x,2)+x*'diff(y,x)+(x2-4)*y=0,y,x)
>
> y = bessel_y(2, x) %k2 + bessel_j(2, x) %k1
>
> but the modified Bessel's will give false
>
> ode2(x2*'diff(y,x,2)+x*'diff(y,x)-(x2+4)*y=0,y,x)
>
> false
>
The second equation is solved by contrib_ode, which is the sandbox
for ode development at present (if I ever get the time ;-( )
%i1) load('contrib_ode)$
(%i2) eq2:x^2*'diff(y,x,2)+x*'diff(y,x)-(x^2+4)*y=0;
2
2 d y dy 2
(%o2) x --- + x -- + (- x - 4) y = 0
2 dx
dx
(%i3) contrib_ode(eq2,y,x);
(%o3) [y = bessel_y(2, - %i x) %k2 + bessel_j(2, - %i x) %k1]