The order of the differential equation \( \left(\displaystyle\frac{d^5y}{dx^5}\right)^2+e^{\frac{dy}{dx}}+y^2=0 \) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5
The order is the order of the highest derivative present. The highest derivative here is \( \frac{d^5y}{dx^5} \), so the order is 5.
Why the other options are incorrect
Option (1) 1 — Incorrect. 1 is the order of \( \frac{dy}{dx} \), but the fifth derivative is also present.
Option (2) Not defined — Incorrect. It is the degree that is not defined here (because of \( e^{dy/dx} \)); the order is always defined.
Option (4) 2 — Incorrect. 2 is the power of the highest derivative, not its order.