Order and degree of derivative

Question

\((\frac{dy}{dx})^2 + \cfrac{1}{\frac{dy}{dx}} = 2\)

Answer 1

\((\frac{dy}{dx})^2 + \cfrac{1}{\frac{dy}{dx}} = 2\)

⇒ \((\frac{dy}{dx})^3\) + 1 = \(2\frac{dy}{dx}\) (Multiply both sides by \(\frac{dy}{dx}\))

⇒ \((\frac{dy}{dx})^3\) - \(2\frac{dy}{dx}\) +1 = 0

which is differential equation in which highest order derivative is \(\frac{dy}{dx}\) and power raised to 3.

\(\therefore\) order = 1 & degree = 3.