Bessel's modified equation



> 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]