The order and degree of the differential equa | vedclass

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Question

(C) Given the differential equation: $ y = x \frac{dy}{dx} + \frac{2}{dy/dx} $.Multiply both sides by $ \frac{dy}{dx} $ to eliminate the fraction:$ y

Vedclass · Accepted Answer

$ 1, 2 $

Vedclass · Answer

(C) Given the differential equation: $ y = x \frac{dy}{dx} + \frac{2}{dy/dx} $.Multiply both sides by $ \frac{dy}{dx} $ to eliminate the fraction:$ y \left( \frac{dy}{dx} \right) = x \left( \frac{dy}{dx} \right)^2 + 2 $.Rearranging the terms,we get: $ x \left( \frac{dy}{dx} \right)^2 - y \left( \frac{dy}{dx} \right) + 2 = 0 $.The highest order derivative present is $ \frac{dy}{dx} $,so the order is $ 1 $.The highest power of the highest order derivative is $ 2 $,so the degree is $ 2 $.Therefore,the order and degree are $ 1 $ and $ 2 $ respectively.

The order and degree of the differential equation $ y = x \frac{dy}{dx} + \frac{2}{dy/dx} $ are

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