Why does the general solution of $y'=y$ not covering $y=0?$ It is regarding the ODE $y'=y.$ 
Usually we try to find its general solution using separation of variables as 
$\frac{dy}{y}=dx\implies\log y=x+c\implies y=e^{x+c}$ ($c$ being arbitrary constants).
Please tell me why does the general solution does not cover the case $y=0.$

$y'=y$ and hence $dy/dx=y$
We need to look at two cases:
When $y=0$ and y$\neq0$
When y=0, the solution is trivially 
$y'=0$. Integration yields $y=A=0$.
Therefore $y=0$ is a solution 
