I have a question concerning, for example, the derivation of the equation for radioactive decay.
You start with the following differential equation $$-\lambda \cdot N=\frac{\mathrm dN}{\mathrm dt}$$
And, after separation of variables and integrating, you obtain $$\int^{t}_{t_0} -\lambda \,\mathrm dt=\int^{N}_{N_0} \frac{1}{N}\,\mathrm dN$$
The right side integrates to $\left[ \ln|N|\right]^{N}_{N_0}$, however the result given in textbooks omits the modulus function. Why can you do that?