At this time, the concentration is multiplied by the change of salt water quantity to get the change of salt content.

The change of salt water quantity is proportional to time, so it can be set to 2dt.

The second horizontal line is the way to separate variables from the first horizontal line.

dx/x= -2dt/( 100+t)

Integrate both sides at the same time, and you get

Lnx=-2ln( 100+t)+X, where x is an arbitrary constant, and it is not written as c here to avoid confusion with the following c.

That is, lnx = ln [e x (100+t) (-2)]

That is, x = c (100+t) (-2) where c = e x.

Get the solution of differential equation