Question

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

• A. \[ \frac32,\;2 \]
• B. \[ 2,\;3 \]
• C. \[ 2,\;2 \]
• D. \[ 3,\;4 \] \bigskip

Hint:

If a differential equation contains radicals or fractional powers of derivatives, first remove them. Then determine the degree from the power of the highest order derivative in the resulting polynomial equation.

Answer 1

The Correct Option is C

Concept: Order is the highest derivative. Degree is the exponent of the highest derivative after clearing radicals/fractions.

Step 1: Given \(\left(1+(dy/dx)^2\right)^{3/2} = d^2y/dx^2\). Highest derivative is \(d^2y/dx^2\): order = 2.

Step 2: Square both sides: \(\left(1+(dy/dx)^2\right)^3 = (d^2y/dx^2)^2\). Exponent of highest derivative is 2: degree = 2.

Step 3: Write the final answer. \(\boxed{(2,\,2)}\)