It is known that we must need to convert the differential equation in polynomial equation of differential coefficients. But Can we differentiate a differential equation (whose degree is not defined) to determine its order and degree ?
Example to show my doubt clearly:
Above differential equation has its degree undefined. Differentiating it with respect to $x$
So we may conclude that this is third order differential equation with degree $=1$
I know that on differentiating a differential equation number of arbitrary constants of solution equation increases hence we should not differentiate a differential equation in general. But I did not found a reference which states that we cannot differentiate a differential equation to determine its order and degree so I want to confirm my thoughts.