Question

The order and degree of the differential equation \[ \left[ 1 + \left( \frac{dy}{dx} \right)^3 \right]^{\frac{3}{2}} = 7 \frac{d^2y}{dx^2} \] are respectively

• A. 2, 1
• B. 2, 3
• C. 1, 2
• D. 3, 2

Hint:

The order is determined by the highest derivative, and the degree is the exponent of the highest derivative after removing fractions and roots.

Answer 1

The Correct Option is B

Step 1: Determine the order.
The order of a differential equation is the highest derivative in the equation. In this case, the highest derivative is \( \frac{d^2y}{dx^2} \), so the order is 2.
Step 2: Determine the degree.
The degree is the exponent of the highest derivative when the equation is made polynomial. The equation contains \( \left( \frac{dy}{dx} \right)^3 \) raised to the power \( \frac{3}{2} \), so after making the equation polynomial by clearing the fraction, the degree is 3.
Step 3: Conclusion.
Thus, the order and degree of the differential equation are 2 and 3, corresponding to option (B).