Wrong solution of differential equation using symbolic lambda

Question

Kevin Oyen 2021-11-23

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1593839-wrong-solution-of-differential-equation-using-symbolic-lambda

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 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 2021-11-23

在 MATLAB Online 中打开

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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Answer 1

Srijith Kasaragod 2021-11-30

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1593839-wrong-solution-of-differential-equation-using-symbolic-lambda#answer_843739

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.