The degree of the differential equation \(y = x\displaystyle\frac{dy}{dx} + \frac{4}{\left(\displaystyle\frac{dy}{dx}\right)}\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2
The degree is read only after the equation is written as a polynomial in the derivatives, so the derivative in the denominator must be cleared first.
Multiplying both sides by \(\frac{dy}{dx}\):
\( \displaystyle y\,\frac{dy}{dx} = x\left(\frac{dy}{dx}\right)^2 + 4 \)
This is a polynomial in \(\frac{dy}{dx}\), the only (and so the highest) derivative. Its highest power is 2, so
\(\text{degree} = 2\)