In general terms for a polynomial the degree is the highest power

The differential equation is

Square both the sides

Now for degree to exist the given differential equation must be a polynomial in some differentials

Here differentials mean

The given differential equation is polynomial in differentials

Degree of differential equation is defined as the highest integer power of highest order derivative in the equation

Here the highest derivative is and there is only one term of highest order derivative in the equation which is whose power is 2 hence degree is 2