This is a trivial question, please note I'm not a professional in this environment, I'm just learning.
Let's suppose I've got this simple eqution:
$L\frac{d i(t)}{dt}=-\frac{1}{C}\int i(t) dt$
I suppose you guess what is, but is not so important: I want to solve it as a differential equation and so I need to remove the integral part. I know that the eq before can be written as:
$\frac{d^2 i(t)}{dt^2}+\frac{1}{LC}i(t) = 0$
It seems to me there is a differentiation of both side of the equation and a division of both sides by L. Is my guess correct ? If so, is it correct to say that differentiating both side of a differenctial equation yield to the same result? I suppose we need to state i(t) being differentiable twice, and maybe there is other restrictions...