Dsolve gives extra term

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Arto Jyvälä
Arto Jyvälä on 16 Nov 2023
Edited: Matt J on 16 Nov 2023
Hello, Im calculating following third term function. I got the following answer without Matlab . However when solving the function with dsolve Matlab gives me this answer .
So my question is, where is this -1/2187 coming from? Is it possible to get rid of it somehow when using dsolve?

Accepted Answer

Matt J
Matt J on 16 Nov 2023
Edited: Matt J on 16 Nov 2023
syms y(x)
eqn = diff(y,x,3)+81*diff(y,x) == 3*x+8;
ytemp(x) = dsolve(eqn);
ysol(x)=dsolve(diff(y,x)==diff(ytemp,x))
ysol(x) = 
  2 Comments
Arto Jyvälä
Arto Jyvälä on 16 Nov 2023
Yes I know you can get rid of it this way. Do you know where the number comes from or can I use some command to remove it?
Matt J
Matt J on 16 Nov 2023
Edited: Matt J on 16 Nov 2023
Do you know where the number comes from
No, not exactly. I speculate dsolve converts this into a 4th order equation and then differentiates the solution to obtain y(x). If the linear terms are not collected together before the final differentiation step, a second constant results.
or can I use some command to remove it?
Yes, you can use the commands in my answer.

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More Answers (1)

John D'Errico
John D'Errico on 16 Nov 2023
Why do you care?
Note that C1 is completely arbirtrary! C1 is an unknown constant!
So you can trivially add or subtract any constant from the result, and the solution is still as valid.
Once you apply initial conditions, then the constant will be absorbed. It will magically go away.
  1 Comment
Arto Jyvälä
Arto Jyvälä on 16 Nov 2023
I have school assignment and I need to check the answer with Matlab. Yes you are right that it goes away if i apply conditions. I was just wondering is it possible to get rid of it somehow.

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