CUET UG 2024 — Mathematics Calculus

First, let's identify that the highest-order derivative is $\frac{d^2y}{dx^2}$dx2d2y​ (second-order).

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Next, we need to eliminate the radical by squaring both sides:
$$\begin{aligned} & {\left[\left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}\right]^{2}=\left[k \frac{d^{2} y}{d x^{2}}\right]^{2}} \\ & \left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{3}=k^{2}\left(\frac{d^{2} y}{d x^{2}}\right)^{2}\end{aligned}$$​​(1−(dxdy​)2)23​​2=[kdx2d2y​]2(1−(dxdy​)2)3=k2(dx2d2y​)2​

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Now the equation is in polynomial form. The highest-order derivative $\frac{d^2y}{dx^2}$dx2d2y​ is raised to the power of 2.

Therefore, the degree of this differential equation is 2.

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Note: The degree is determined by the highest power of the highest-order derivative after converting to polynomial form. Don't confuse this with the order of the equation (which is also 2 in this case).