CUET UG 2025 — Mathematics Calculus

Given equation:

$$\sqrt{1 + \left(\frac{dy}{dx}\right)^2} = \left[a \frac{d^2y}{dx^2}\right]^{\frac{1}{2}}$$1+(dxdy​)2​=[adx2d2y​]21​

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The order of a differential equation is determined by the highest derivative present in the equation.

Examining the equation, the derivatives present are:

$\frac{dy}{dx}$dxdy​ (first derivative)

$\frac{d^2y}{dx^2}$dx2d2y​ (second derivative)

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The highest derivative in the equation is the second derivative $\frac{d^2y}{dx^2}$dx2d2y​.

The square roots and powers do not affect the order. Order only depends on the highest derivative present.

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Therefore, the order of the differential equation is $2$2.