Question

If 'a' and 'b' are the order and degree respectively of the differentiable equation \[ \frac{d^2 y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + x^4 = 0, \quad \text{then} \, a - b = \, \_ \_ \]

• A. 2
• B. -1
• C. 0
• D. 1

Hint:

The order of a differential equation is the highest order of the derivative, and the degree is the highest power of the highest derivative.

Answer 1

The Correct Option is C

The given differential equation is: \[ \frac{d^2 y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + x^4 = 0 \] - The order of the equation is the highest derivative present, which is \( \frac{d^2 y}{dx^2} \), so the order \( a = 2 \). - The degree of the equation is the power of the highest derivative term, \( \left(\frac{dy}{dx}\right)^3 \), so the degree \( b = 2 \). Thus, \( a - b = 2 - 2 = 0 \).