The sum of the degree and order of the following differential equation [1- ( d y d x )^2 ]^ 3 2 =k x d^2 y d x^2

Step-by-step solution

The given differential equation is [1 - ( dy dx )^2 ]^ 3 2 = kx d^2y dx^2 . To determine the order and degree, the equation must be expressed as a polynomial in terms of the derivatives. Squaring both sides to eliminate the fractional exponent, we get: [1 - ( dy dx )^2 ]^3 = (kx)^2 ( d^2y dx^2 )^2 . The order of the differential equation is the highest derivative present, which is d^2y dx^2 . Thus, the order is 2. The degree of the differential equation is the power of the highest order derivative when the equation