Complex Numbers Quiz -1

Quiz: Degree and Order of ODEs (2025)

1. What is the order of the differential equation \( \frac{d^3y}{dx^3} + 2\frac{dy}{dx} = 0 \)?
   A. 1
   B. 2
   C. 3
   D. 4
   
2. What is the degree of the equation \( \left( \frac{d^2y}{dx^2} \right)^2 + \frac{dy}{dx} = y \)?
   A. 1
   B. 2
   C. 0
   D. Not defined
   
3. What is the order of \( \left( \frac{d^2y}{dx^2} \right)^3 + y = 0 \)?
   A. 1
   B. 2
   C. 3
   D. 0
   
4. Find the degree of the differential equation \( \frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^2 = 0 \).
   A. 1
   B. 2
   C. 3
   D. Not defined
   
5. What is the degree of \( \frac{d^2y}{dx^2} + \sqrt{\frac{dy}{dx}} = 0 \)?
   A. 1
   B. 2
   C. Not defined
   D. 0
   
6. Which of the following has order 1 and degree 2?
   A. \( \left( \frac{dy}{dx} \right)^2 + y = 0 \)
   B. \( \frac{d^2y}{dx^2} + y = 0 \)
   C. \( \frac{dy}{dx} + y = 0 \)
   D. \( \left( \frac{d^2y}{dx^2} \right)^2 + y = 0 \)
   
7. The order of \( y'' + y'^2 + y = 0 \) is:
   A. 1
   B. 2
   C. 3
   D. 0
   
8. Which of the following differential equations does NOT have a defined degree?
   A. \( \frac{d^2y}{dx^2} + \frac{dy}{dx} = y \)
   B. \( \frac{d^3y}{dx^3} + y = 0 \)
   C. \( \frac{d^2y}{dx^2} + \sin\left(\frac{dy}{dx}\right) = 0 \)
   D. \( \left( \frac{dy}{dx} \right)^3 + y = 0 \)
   
9. The equation \( \frac{d^4y}{dx^4} + y = 0 \) has:
   A. Order 3, Degree 1
   B. Order 4, Degree 1
   C. Order 4, Degree 4
   D. Order 1, Degree 4
   
10. What is the order and degree of the equation \( \left( \frac{d^3y}{dx^3} \right)^2 + e^{\left( \frac{dy}{dx} \right)^2} = 0 \)?
    A. Order 3, Degree is not defined
    B. Order 3, Degree 2
    C. Order 2, Degree is not defined
    D. Order 2, Degree 2