Wrong solution of differential equation using symbolic lambda

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Kevin Oyen
Kevin Oyen 2021-11-23
编辑： Srijith Kasaragod 2021-12-2
As can be seen in the screenshot I have a problem with the symbol lambda in matlab R2021B. If lambda is used instead of the variable L, a wrong solution for the differential equation is obtained. What can be the cause for this problem? Many thanks in advance!
clear all
syms R(r) L
assume(L, "real")
assume(L > 0)
vgl = r*diff(R(r),2,r) + diff(R(r),1,r) == L*r*R(r)
dsolve(vgl)
clear all
syms R(r) lambda
assume(lambda, "real")
assume(lambda > 0)
vgl = r*diff(R(r),2,r) + diff(R(r),1,r) == lambda*r*R(r)
dsolve(vgl)
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Kevin Oyen
Kevin Oyen 2021-11-23
Thanks for your answer. I'm sorry, it's the first time I post something here... The code is in there and it is in Matlab R2021B, cause I needed to fill it in to submit the question I thought you could see it also.
Paul
Paul 2021-11-23
Ran in:
I don't have an answer, but the result seems (strangely) to depend on the case (upper or lower) of the first character of the variable. Is there way you can check if the solutions are equivalent? I wasn't sure how to choose the Ci.
syms R(r) L
assume(L, "real")
assume(L > 0)
vgl = r*diff(R(r),2,r) + diff(R(r),1,r) == L*r*R(r);
dsolve(vgl)
ans = 
syms R(r) lambda
assume(lambda, "real")
assume(lambda > 0)
vgl = r*diff(R(r),2,r) + diff(R(r),1,r) == lambda*r*R(r);
dsolve(vgl)
ans = 
syms R(r) Lambda
assume(Lambda, "real")
assume(Lambda > 0)
vgl = r*diff(R(r),2,r) + diff(R(r),1,r) == Lambda*r*R(r);
dsolve(vgl)
ans = 
syms R(r) AAA
assume(AAA, "real")
assume(AAA > 0)
vgl = r*diff(R(r),2,r) + diff(R(r),1,r) == AAA*r*R(r);
dsolve(vgl)
ans = 
syms R(r) aAA
assume(aAA, "real")
assume(aAA > 0)
vgl = r*diff(R(r),2,r) + diff(R(r),1,r) == aAA*r*R(r);
dsolve(vgl)
ans = 

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采纳的回答

Srijith Kasaragod
Srijith Kasaragod 2021-11-30
编辑：Srijith Kasaragod 2021-12-2
Hi Kevin,
This is a bug and has been brought to the notice of our developers. It may be fixed in future releases. One possibility to resolve this problem would be to avoid solutions using the imaginary unit in representation, which in this case would prefer the representation using besseli and besselk functions.
Regards,
Srijith.
  1 个评论
Paul
Paul 2021-11-30
@Srijith Kasaragod
Can you better describe what the bug actually is? What is the title and description of the bug? Is there a link to a bug report?

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