hello, need your help

find all function $\displaystyle f$ differentiable over $\displaystyle \mathbb{R}$

$\displaystyle - (\forall x\in \mathbb{R}) : \big(f'(x)\big)^2-\big(f(x)\big)^2=1 \quad (1) $

$\displaystyle -f'(0)=1 \quad(2)$

$\displaystyle -f'$ is differentiable over $\displaystyle \mathbb{R}\quad (3)$