The degree of the differential equation \(\displaystyle\frac{d^2y}{dx^2}+\left(\frac{dy}{dx}\right)^3= \left(\frac{d^3y}{dx^3}\right)^2\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
The equation is a polynomial in the derivatives, so its degree can be read directly.
The highest order derivative is \(\frac{d^3y}{dx^3}\), so the order is 3.
The degree is the highest power of this highest order derivative. \(\frac{d^3y}{dx^3}\) appears with power 2, so the degree is 2.
The power 3 belongs to \(\frac{dy}{dx}\), a lower order derivative, so it does not decide the degree.