Order And Degree

Order and degree describe the structural complexity of a differential equation: the order is the highest derivative present, while the degree is the power of that highest-order derivative once the equation is written as a polynomial in derivatives free of radicals and fractions. Here the highest derivative appearing is \frac{d^2y}{dx^2}, so the order is unambiguously 2. The equation is already polynomial in the derivatives and contains no fractional powers or radicals on any derivative term, so the degree is simply the exponent attached to that highest derivative, namely the power 3 in \left(\frac{d^2y}{dx^2}\right)^3. The presence of \left(\frac{dy}{dx}\right)^5 does not influence the degree, because degree is defined only by the highest-order derivative, not by lower-order ones. Option Order 2, Degree 5 incorrectly reads the fifth power of the first derivative as the degree. Option Order 3, Degree 2 misidentifies the highest derivative as a third derivative. Option Order 2, Degree 1 ignores the cubic power entirely. This follows the standard JEE Advanced definition of degree for polynomial-form equations. As a final consistency check, the equation is genuinely polynomial in its derivatives, so degree is well defined, and the highest derivative carrying exponent 3 confirms the pairing order 2 and degree 3.