The order and degree of the differential equation $y = \frac{dy}{dx} + \sqrt{a^{2}\left( \frac{dy}{dx} \right)^{2} + b^{2}}$ is

Question

Dr. Abubacker · Accepted Answer

(b)
Given differential equation can be rewritten as
$y - x\ \frac{dy}{dx} = \sqrt{a^{2}\ \left( \frac{dy}{dx} \right)^{2} + b^{2}}$
$\Rightarrow$ $y^{2} + \left( x\ \frac{dy}{dx} \right)^{2} - 2yx\ \frac{dy}{dx} = a^{2}\left( \frac{dy}{dx} \right)^{2} + b^{2}$
Here, order is 1 and degree is 2.

Q. The order and degree of the differential equation $y = \frac{dy}{dx} + \sqrt{a^{2}\left( \frac{dy}{dx} \right)^{2} + b^{2}}$ is

Explanation

Reviewed by Dr. Abubacker

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