What is the degree of the differential equation ( d^2y dx^2 )^ 3 2 = ( dy dx )^ 5 2 ?

Step-by-step solution

The given differential equation is ( d^2y dx^2 )^ 3 2 = ( dy dx )^ 5 2 . To find the degree of the differential equation, the powers of the derivatives must be made integers. Squaring both sides, we get: ( d^2y dx^2 )^3 = ( dy dx )^5 The highest order derivative is d^2y dx^2 , which has an order of 2 . The power of the highest order derivative is 3 . Therefore, the degree of the differential equation is 3 .