COMEDK 2025 Afternoon Solved Paper

Concept:The degree of a differential equation is the power of the highest-order derivative after removing radicals and fractional exponents.Explanation:Start with the given equation:$\left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{4}} = \left(\frac{d^2 y}{dx^2}\right)^{\frac{1}{3}}$To eliminate the fractional powers, raise both sides to the least common multiple of the denominators $4$ and $3$, which is $12$:$\left[\left[1+(y')^2\right]^{\frac{3}{4}}\right]^{12} = \left[(y'')^{\frac{1}{3}}\right]^{12}$This simplifies to:$\left[1+(y')^2\right]^{9} = (y'')^{4}$Now the equation is a polynomial in derivatives. The highest-order derivative is $y''$ (second order), and its power is $4$.Therefore, the degree of the differential equation is $4$.Answer:$4$ (Option A)