[Maxima] Bessel's modified equation

[Barton Willis]

Odelin will solve this DE; try

 (%i3) load(odelin)$

 (%i6) odelin(x^2*'diff(y,x,2)+x*'diff(y,x)-(x^2+4)*y=0,y,x);
 (%o6) {bessel_j(2,-%i*x),bessel_y(2,-%i*x)}

Notice that odelin gives a fundamental solution set, not a general
solution.

Barton

-----maxima-bounces at math.utexas.edu wrote: -----


>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]
>
>
>
>_______________________________________________
>Maxima mailing list
>Maxima at math.utexas.edu
>http://www.math.utexas.edu/mailman/listinfo/maxima