Quick diff eq question

[kdinser]

I'm pretty sure I know the answer to this, just want to double check.

For the problems that I'm currently working on, we are just solving the problems for an unknown constant C.

I just finished one were I came up with
\frac{x^2}{2}-y^2cos x-xy^3=C

The book shows the solution as
y^2cos x+xy^3-\frac{x^2}{2}=C

Because C is an arbitrary, unknown constant, did they just multiply both sides by -1? Is there some reason for doing this other then getting rid of 2 negatives in the answer?

[dextercioby]

It's irrelevant which solution u chose,u can verify that both satisfy the same diff.eq.,the one which u were supposed to solve.In general,a smaller number of minuses is preferable.Par éxample:
x+y=4
would u like it more than
-x-y=-4

??

Daniel.