Question

The order of the differential equation $\left(\dfrac{d^{3}y}{dx^{3}}\right)^{2} + x^{2}\left(\dfrac{d^{2}y}{dx^{2}}\right)^{3} + 7y = \sin x$ will be:

• A. $2$
• B. $3$
• C. $5$
• D. $6$

Hint:

Order of a differential equation = highest order of derivative present (ignore powers or exponents).

Answer 1

The Correct Option is B

Step 1: Recall definition of order.
The order of a differential equation is the order of the highest derivative present in the equation.

Step 2: Identify highest derivative.
In the given equation: \[ \left(\frac{d^{3}y}{dx^{3}}\right)^{2} + x^{2}\left(\frac{d^{2}y}{dx^{2}}\right)^{3} + 7y = \sin x \] The highest derivative is $\dfrac{d^{3}y}{dx^{3}}$.

Step 3: Ignore powers for order.
Even though $\left(\dfrac{d^{3}y}{dx^{3}}\right)$ is squared, the order depends only on the derivative itself, not its power.

Step 4: Conclusion.
Hence, the order of the differential equation is $3$. The correct answer is (B).