The degree of the differential equation d ^2 y d x^2 +3 ( ~d y ~d x )^2=x^2 ( ~d ^2 y d x^2 ) is

Step-by-step solution

The differential equation d^2y dx^2 + 3 ( dy dx )^2 = x^2 ( d^2y dx^2 ) contains a logarithmic function of the second derivative. Since logarithmic functions cannot be expressed as polynomials in their arguments, this equation is not a polynomial in its derivatives. Consequently, the degree of this differential equation is undefined. Final answer: D