The degree of the differential equation 1 + ( dy dx )^ 1/3 = d^2y dx^2 is:

Step-by-step solution

Given differential equation is 1 + ( dy dx )^ 1/3 = d^2y dx^2 Squaring both sides, we get 1 + ( dy dx )^ 1/3 = ( d^2y dx^2 )^2 Rearranging the terms, ( dy dx )^ 1/3 = ( d^2y dx^2 )^2 - 1 Cubing both sides to make the powers of derivatives integers, dy dx = [ ( d^2y dx^2 )^2 - 1 ]^3 The highest order derivative is d^2y dx^2 and its highest power in the polynomial equation is 2 3 = 6 . Therefore, the degree of the differential equation is 6 . Answer: 6