Bessel's modified equation

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