Is this proof for a linear differential eq correct purely mathematically

1. Oct 29, 2007

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

2. Oct 29, 2007

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.

3. Oct 29, 2007

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 ...