The order and degree of the differential equation 1 + 1 ( dy dx )^2 = ( d^2y dx^2 )^ 3 2 , respectively are

Step-by-step solution

The given differential equation is 1 + 1 ( dy dx )^2 = ( d^2y dx^2 )^ 3 2 Squaring both sides to remove the fractional powers, we get: 1 + 1 ( dy dx )^2 = ( d^2y dx^2 )^3 Multiplying the entire equation by ( dy dx )^2 to express it as a polynomial in derivatives: ( dy dx )^2 + 1 = ( dy dx )^2 ( d^2y dx^2 )^3 The highest order derivative present in the equation is d^2y dx^2 , which means the order of the differential equation is 2 . The power of the highest order derivative in this polynomial form is 3 , which means