Question

The order of the differential equation \(x\left(\dfrac{d^3y}{dx^3}\right)^2+\sin x\left(\dfrac{d^2y}{dx^2}\right)^3+\left(\dfrac{dy}{dx}\right)^4+y^5=0\) is

• A. 2
• B. 3
• C. 5
• D. 6

Hint:

Order = highest derivative level present, ignoring the powers on each term.

Answer 1

The Correct Option is B

Step 1: Common confusion check:
The exponent 2 on \(\left(\dfrac{d^3y}{dx^3}\right)^2\) is the *degree* contribution, not the order — order never depends on powers/exponents.

Step 2: Re-reading only derivative levels:
Ignoring all powers, the derivative levels present are 3rd, 2nd and 1st order; the largest is 3.

Final Answer:
\[ \boxed{3} \]