here is one ODE I solved now

[tex]

y' = 1 + y^2

[/tex]

So

[tex]

\frac{y'}{1+y^2} = 1

[/tex]

[tex]

\int \frac{dy}{1+y^2} = \int 1 dx

[/tex]

[tex]

\arctan y = x + C \leftrightarrow y = \tan (x + C)

[/tex]

[tex]

x \in (-\frac{\pi}{2} - C, \frac{\pi}{2} - C)

[/tex]

The last line is what I'm unsure about.

Shouldn't it rather be

[tex]

x \in (-\frac{\pi}{2} - C + k\pi, \frac{\pi}{2} - C + k\pi), k \in \mathbb{Z}

[/tex]

or is it ok as I wrote it originally?

Thank you.