Dsolve gives extra term

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?

Answer 1

[Matt J]

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) = 

[Arto Jyvälä]

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]

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.

Answer 2

[John D'Errico]

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.

[Arto Jyvälä]

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.