Question

The order and degree of the differential equation \[ \left(\frac{d^2y}{dx^2}\right)^3+\left(\frac{dy}{dx}\right)^2+y=0 \] are respectively:

• A. $2,3$
• B. $3,2$
• C. $2,2$
• D. $3,3$

Hint:

Order depends only on the highest derivative present, whereas degree depends on the power of that highest derivative after simplifying the equation into polynomial form.

Answer 1

The Correct Option is A

Understanding the Concept:
The order of a differential equation is the order of the highest derivative present.
The degree is the power of the highest order derivative after the equation is free from radicals and fractional powers.

Step 1: Identify the highest order derivative.
The equation is: \[ \left(\frac{d^2y}{dx^2}\right)^3+\left(\frac{dy}{dx}\right)^2+y=0 \] The highest derivative present is: \[ \frac{d^2y}{dx^2} \] Hence, \[ \text{Order}=2 \]
Step 2: Determine the degree.
The highest order derivative appears as: \[ \left(\frac{d^2y}{dx^2}\right)^3 \] The power is: \[ 3 \] Therefore, \[ \text{Degree}=3 \] Hence, \[ \boxed{(2,3)} \]