Question

The sum of the order and degree of the differential equation $ \left( \frac{d^5y}{dx^5} \right) + 4 \left( \frac{d^4y}{dx^4} \right) + \left( \frac{d^3y}{dx^3} \right) = x^2 - 1 $

• A. 4
• B. 5
• C. 6
• D. 8

Hint:

To find the order and degree of a differential equation, identify the highest order derivative for the order and ensure that there are no fractional or irrational exponents for the degree.

Answer 1

The Correct Option is B

The given differential equation is: \[ \left( \frac{d^5y}{dx^5} \right) + 4 \left( \frac{d^4y}{dx^4} \right) + \left( \frac{d^3y}{dx^3} \right) = x^2 - 1 \] The order of the differential equation is determined by the highest order of the derivative. 
In this case, the highest order derivative is \( \frac{d^5y}{dx^5} \), so the order is 5. 
The degree of a differential equation is the exponent of the highest order derivative, provided that the equation is free from any fractional powers or irrational expressions in derivatives. 
In this case, the highest order derivative is \( \frac{d^5y}{dx^5} \), and its exponent is 1 (since it is not raised to any power). 
So, the degree is 1. Thus, the sum of the order and degree is: \[ \text{Order} + \text{Degree} = 5 + 1 = 5 \] 
Thus, the correct answer is \( (B) 5 \).