For the differential equation \(\displaystyle\frac{d^2y}{dx^2} = x + \tan\left(\frac{dy}{dx}\right)\), which of the following is true?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → order 2, degree not defined
The highest derivative present is \(\frac{d^2y}{dx^2}\), so
\(\text{order} = 2\)
The degree is defined only when the equation is a polynomial in the derivatives. Here \(\frac{dy}{dx}\) sits inside \(\tan\), and \(\tan\left(\frac{dy}{dx}\right)\) is not a polynomial in \(\frac{dy}{dx}\).
So the degree is not defined, even though the order is 2.