Mathematica Is this proof for a linear differential eq correct purely mathematically

[Pellefant]

Is this proof for a "linear differential eq" correct purely mathematically

I wonder if this proof is correct purely mathematically
look at (3) in the link, and you will se that they have done the following ...

\int p(x)dx = \int p(x)dx +c

So they have put out the constant of integration before they have done the integration, can they really do that?

http://www.bio.brandeis.edu/classes/biochem102/hndDiffEq.pdf

 

[andytoh]

Yes, since constant + constant = constant. They probably did that to emphasize that a constant will have to be worked out to fit some initial conditions.

 

[Pellefant]

Yea it makes it much easier because then you don't need to think about constant of integration ... In my brain i can see that as mathematically correct if c=0 because e^0=1 ...

I am fairly sure that you can't say c1+c=c2, for a value where c isn't cero, because the value from the integration (which gives c1) can just be the exactly correct value form that integration ...

Sorry if i am concerned about stuff that don't matter, but for me it is important for my understanding ...

Kindly Pellefant ...