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Re: Bessel And Airy Functions in Solutions

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On 04/03/14 21:17, Thomas D. Dean wrote:

I am making some progress.  I can now recognize the results as similar.

maxima := y(x) = BesselY(1/3,2*(a*x+b)^(3/2)/(3*abs(a)))*_C12*sqrt(a*x+b)
+BesselJ(1/3,2*(a*x+b)^(3/2)/(3*abs(a)))*_C11*sqrt(a*x+b);
convert(maxima,Airy);
collect(%, [AiryAi, AiryBi]):
simplify(%, size);
maxima2:=%;
maxima3:=subs({-_C12-sqrt(3)*_C11/3=_C2,-_C12*sqrt(3)/3+_C11=_C1},maxima2);

ode:=diff(y(x),x,x)+(a*x+b)*y(x)=0;
raw_soln:=dsolve(ode);

subs(raw_soln,ode);
evala(%,diff);
expand(%);

subs(maxima3,ode);
evala(%,diff);
expand(%);
collect(%, [AiryAi, AiryBi]):
simplify(%, size);

raw_soln; subs({K1=_C2,K2=_C1},maxima3);

If I can reduce
((a*x+b)^(3/2)/abs(a))^(2/3);
to
(a*x+b)/a^(2/3);
I will be within a factor of 1/abs(a).

Tom Dean

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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

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