The degree of a DE is defined only when the equation is a polynomial in all its derivatives. Key cases where degree IS defined: (y')^3 + y'' = x (degree 1 in y'', which is the highest order). (y'')^2 + (y')^5 = $x^3$ (degree 2). Key cases where degree is NOT defined: y' = sin(y'') (transcendental function of y''). e^(y') = x (exponential of derivative). y'' = (1 + y'^2)^$\frac{3}{2}$ (fractional power of expression containing derivatives). However, (y'')^2 = (1 + y'^2)^3 DOES have defined degree (= 2) because both sides are polynomial. The distinction: in the original form, if any derivative appears inside a non-polynomial function, degree is undefined.