Question

The order and degree of the differential equation \(3-(\frac{\text{d}^3y}{\text{d}x^3})^{\frac{7}{3}} = (\frac{\text{d}y}{\text{d}x})^5\) are respectively

• A. \(3,7\)
• B. \(7,3\)
• C. \(5,7\)
• D. \(3,5\)

Hint:

Clear the fractional power by isolating the radical term and raising both sides to a power.

Answer 1

The Correct Option is A

Step 1: Highest derivative
$d^3y/dx^3$ appears, so order is 3.

Step 2: Polynomial form
Moving the fractional power alone to one side and cubing gives $(y''')^7 = (3 - y'^5)^3$.

Step 3: Degree
The power of $y'''$ is 7. So (order, degree) $= (3, 7)$, option (A).

Final Answer:
Option (A). \[ \boxed{3, 7} \]