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: Definition of order:
The order of a differential equation is the order of the highest derivative appearing in it, regardless of the power it is raised to.

Step 2: Scanning the equation:
The derivatives present are \(\dfrac{d^3y}{dx^3}\) (third order), \(\dfrac{d^2y}{dx^2}\) (second order) and \(\dfrac{dy}{dx}\) (first order).

Step 3: Picking the highest:
The highest-order derivative present is \(\dfrac{d^3y}{dx^3}\).

Final Answer:
\[ \boxed{\text{Order}=3} \]