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UPSC NDA II 2025 Mathematics Paper

Question : 91 of 120

Marks: +1, -0

(\frac{d^{2}y}{dx^{2}})^{\frac{3}{2}}=(\frac{dy}{dx})^{\frac{5}{2}}

Solution:

Concept:

Degree of a differential equation is the power of the highest order derivative after the equation is free from radicals and fractions.

Explanation:

Given equation:

(\frac{d^{2}y}{dx^{2}})^{\frac{3}{2}} = (\frac{dy}{dx})^{\frac{5}{2}}

To remove the fractional powers, square both sides:

(\frac{d^{2}y}{dx^{2}})^{3} = (\frac{dy}{dx})^{5}

The highest order derivative is

\frac{d^{2}y}{dx^{2}}

and its power is 3.

Thus, the degree is 3.

Answer:

A. 3

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