Originally Posted by

**superdude** I have a question with regards to another differential problem:

$\displaystyle \frac{dy}{dx}=\frac{(ycosx)}{(1+y^2)}$

$\displaystyle \Rightarrow \frac{1+y^2}{y} dy = \frac{ycosx}{y} dx$

$\displaystyle \Rightarrow \int \frac{1}{y} dy+\int y dy = \int cosx dx$

$\displaystyle \Rightarrow lny+\frac{y^2}{2} {\color{red}+C} = sinx+C$

why is it wrong to have the +C there? The second part of the question says for y(0)=1 find a specific formula. I know the way I have it setup with C on both sides they will always cancel off, but it seems somewhat logical considering how if it maters which side of the equation I put C on. For example, on the right it is +1 but if I left the +C and took the other away it would be -1.