Can You Choose Your Own Constants in Differential Equations Integration?

[gomes.]

On this page below, the person chooses the constants to be anything they want, but can you actually do that?
Pauls Online Notes : Differential Equations - Reduction of Order

 

[rock.freak667]

Because it makes the coefficient of the term with t as 1 and 0 as the constant. It sort of makes the obtained general solution 'better' looking.

 

[gomes.]

thanks, so you are allowed to set it to any number?

 

[rock.freak667]

For that, it looks that way. Granted I did not really read through the equations thoroughly.