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UPSC NDA Math Model Paper 10

Question : 2 of 120

Marks: +1, -0

y = x \frac{dy}{dx} + \left( \frac{dy}{dx} \right)^{-2} ?

Solution:

Given:

y = x \frac{dy}{dx} + \left( \frac{dy}{dx} \right)^{-2} y

= x dx + \frac{1}{\left( \frac{dy}{dx} \right)^2} y \left( \frac{dy}{dx} \right)^2

= x \left( \frac{dy}{dx} \right)^3 + 1

For the given differential equation the highest order derivative is 1.

Now, the power of the highest order derivative is 3.

We know that the degree of a differential equation is the power of the highest derivative.

Hence, the degree of the differential equation is 3.

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