Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.soft-sys.math.maple > #870

Re: Bessel And Airy Functions in Solutions

Followups directed to: sci.math.symbolic

Show all headers | View raw

On 04.04.2014 06:17, Thomas D. Dean wrote:
> I have a problem,
>
> ode:=diff(y(x),x,x)+(a*x+b)*y(x)=0;
> raw_soln:=dsolve(ode);
> soln1:=convert(raw_soln,BesselI);
>
> This gives an expression with several terms.
>
> Maxima gives a solution,
>
> [y = bessel_y(1/3,2*(a*x+b)^(3/2)/(3*abs(a)))*%k2*sqrt(a*x+b)
>            +bessel_j(1/3,2*(a*x+b)^(3/2)/(3*abs(a)))*%k1*sqrt(a*x+b)]
> where bessel_y is the second kind and bessel_j is the first kind.
>
> If I assume %k2 is _C2 and %k1 is _C1
>
> maxima := y(x) = BesselY(1/3,2*(a*x+b)^(3/2)/(3*abs(a)))*_C2*sqrt(a*x+b)
>      +BesselJ(1/3,2*(a*x+b)^(3/2)/(3*abs(a)))*_C1*sqrt(a*x+b);
> soln2:=convert(maxima,BesselI);
>
> I am having problems determining if these are the same.
>
> Ideas?
>
> Tom Dean

Better use different constants for Maxima's solution. And convert
to Airy functions. Then comparing the inputs for the Airy functions
show different expressions. May be you need 0 < a to get the 'same'
as your raw_solution

   convert(maxima, Airy):
   collect(%, [AiryAi, AiryBi]):
   simplify(%, size);
   maxima2:=%;

Back to comp.soft-sys.math.maple | Previous | Next — Previous in thread | Next in thread | Find similar

Thread

Bessel And Airy Functions in Solutions "Thomas D. Dean" <tomdean@speakeasy.org> - 2014-04-03 21:17 -0700
  Re: Bessel And Airy Functions in Solutions Axel Vogt <&noreply@axelvogt.de> - 2014-04-04 11:53 +0200
  Re: Bessel And Airy Functions in Solutions "Thomas D. Dean" <tomdean@speakeasy.org> - 2014-04-04 11:28 -0700

csiph-web