While solving separable differential equation 
g(y)#card=math&code=%5Cfrac%7Bd%20y%7D%7Bd%20x%7D%20%3D%20f%28x%29g%28y%29&id=klNtf) with 
%3Da_1%20y%20%2B%20a_0#card=math&code=g%28y%29%3Da_1%20y%20%2B%20a_0&id=kMtw8) is a polynomial of degree one, then 
, and 
%7D%20%3D%20f(x)%5C%2C%20dx%20%3D%20%5Cfrac%7Bdy%7D%7Ba_1%20y%20%2Ba_0%7D#card=math&code=%5Cfrac%7Bdy%7D%7Bg%28y%29%7D%20%3D%20f%28x%29%5C%2C%20dx%20%3D%20%5Cfrac%7Bdy%7D%7Ba_1%20y%20%2Ba_0%7D&id=WLN9E).
Integration:
.
We see that the natural exponential and/or logarithmic functions come out naturally while solving ODE derived from physical/natural laws. This is an important reason to call them “natural”.
