The order and degree of the differential equation are respectively:
The order and degree of the differential equation
are respectively:
Answer: A. 3 and 2 — Order: The highest derivative present is d^3y/dx^3, so the order is 3. Degree: The degree is the power of the highest order derivative when the differential…
- A.
3 and 2
- B.
2 and 3
- C.
3 and 3
- D.
3 and 1
Attempted by 29 students.
Show answer & explanation
Correct answer: A
Order: The highest derivative present is d^3y/dx^3, so the order is 3.
Degree: The degree is the power of the highest order derivative when the differential equation is expressed as a polynomial in derivatives (after eliminating any radicals or fractional powers).
Reasoning:
The given equation contains the term sqrt((dy/dx)^3) which equals (dy/dx)^(3/2). This is a fractional (non‑polynomial) power of a derivative.
To determine degree we first remove fractional powers. If we eliminate the square root by squaring the entire equation, the highest derivative term d^3y/dx^3 becomes (d^3y/dx^3)^2 in the resulting polynomial expression.
After this operation the highest order derivative appears raised to the power 2, so the degree is 2.
Conclusion: The order is 3 and the degree is 2.