$\frac{dy}{dx} = \left[y + \left(\frac{dy}{dx}\right)\right]^{1/4}$
Step-by-Step Solution
Key Concept: Order of a differential equation is determined by the highest derivative present; degree is the power of that highest derivative when the equation is polynomial in derivatives
Raising both sides of the differential equation to the fourth power: $\left(\frac{dy}{dx}\right)^4 = y + \left(\frac{dy}{dx}\right)$. This can be rewritten as $\left(\frac{dy}{dx}\right)^4 - \frac{dy}{dx} - y = 0$. The highest derivative appearing is $\frac{dy}{dx}$ with power 4, indicating degree 4, while the derivative itself is first-order. Therefore the order is 1 and the degree is 4.
Correct Answer: 2