Order and degree of differential equations MCQs With Answer

Introduction: Understanding the order and degree of differential equations is essential for B.Pharm students studying pharmacokinetics, drug release modeling, and formulation mathematics. This concise guide on “Order and degree of differential equations MCQs With Answer” focuses on identifying the highest derivative (order) and the power of that derivative when the equation is a polynomial in derivatives (degree). Clear definitions, typical exam-style examples, and special cases—like transcendental functions or fractional powers—are emphasized to build practical problem-solving skills. Keywords: order and degree of differential equations, B.Pharm, MCQs with answers, pharmaceutical mathematics, ODE classification. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the order and degree of the differential equation d^2y/dx^2 + (dy/dx)^2 = 0?

Order 2, Degree 1
Order 2, Degree 2
Order 1, Degree 2
Order 2, Degree undefined

Correct Answer: Order 2, Degree 1

Q2. What is the order and degree of the equation (d^3y/dx^3) + 5y = 0?

Order 2, Degree 1
Order 3, Degree 1
Order 3, Degree 3
Order 1, Degree 3

Correct Answer: Order 3, Degree 1

Q3. Determine the order and degree of sin(dy/dx) + y = 0.

Order 1, Degree 1
Order 1, Degree undefined
Order undefined, Degree 1
Order 2, Degree undefined

Correct Answer: Order 1, Degree undefined

Q4. Find the order and degree of (d^2y/dx^2)^3 + (dy/dx) = 0.

Order 2, Degree 3
Order 2, Degree 1
Order 3, Degree 2
Order 2, Degree undefined

Correct Answer: Order 2, Degree 3

Q5. What is the order and degree of y” + e^{dy/dx} = 0?

Order 2, Degree 1
Order 2, Degree undefined
Order 1, Degree undefined
Order 2, Degree 2

Correct Answer: Order 2, Degree undefined

Q6. For the equation (d^2y/dx^2)^{1/2} + y = 0, the order and degree are:

Order 2, Degree 1
Order 2, Degree undefined
Order 1, Degree 2
Order 2, Degree 1/2

Correct Answer: Order 2, Degree undefined

Q7. Identify order and degree: d^4y/dx^4 + (d^2y/dx^2)^2 = 0.

Order 4, Degree 1
Order 4, Degree 2
Order 2, Degree 2
Order 4, Degree undefined

Correct Answer: Order 4, Degree 1

Q8. What are the order and degree of the differential equation dy/dx + y = 0?

Order 1, Degree 1
Order 1, Degree undefined
Order 0, Degree 1
Order 2, Degree 1

Correct Answer: Order 1, Degree 1

Q9. Determine order and degree: (d^3y/dx^3)^2 + (dy/dx) = 0.

Order 3, Degree 2
Order 3, Degree 1
Order 2, Degree 2
Order 3, Degree undefined

Correct Answer: Order 3, Degree 2

Q10. For y” + (sin y”) = 0, the order and degree are:

Order 2, Degree 1
Order 2, Degree undefined
Order 1, Degree undefined
Order 2, Degree 2

Correct Answer: Order 2, Degree undefined

Q11. What is the order and degree of dy/dx = x^2?

Order 1, Degree 0
Order 1, Degree 1
Order 2, Degree 1
Order 1, Degree undefined

Correct Answer: Order 1, Degree 1

Q12. Determine order and degree: d^2y/dx^2 + (dy/dx)^3 – y = 0.

Order 2, Degree 3
Order 2, Degree 1
Order 3, Degree 3
Order 2, Degree undefined

Correct Answer: Order 2, Degree 3

Q13. For the equation y”’ + ln(dy/dx) = 0, the order and degree are:

Order 3, Degree undefined
Order 1, Degree undefined
Order 3, Degree 1
Order undefined, Degree undefined

Correct Answer: Order 3, Degree undefined

Q14. What is the order and degree of (d^2y/dx^2)/(dy/dx) + y = 0?

Order 2, Degree 1
Order 2, Degree undefined
Order 1, Degree 1
Order 2, Degree -1

Correct Answer: Order 2, Degree undefined

Q15. Identify order and degree: d^5y/dx^5 – 3(d^2y/dx^2)^4 = 0.

Order 5, Degree 1
Order 5, Degree 4
Order 2, Degree 4
Order 5, Degree undefined

Correct Answer: Order 5, Degree 1

Q16. For the equation (d^2y/dx^2) + (dy/dx)^{1/2} = 0, order and degree are:

Order 2, Degree undefined
Order 2, Degree 1/2
Order 1, Degree 1
Order 2, Degree 1

Correct Answer: Order 2, Degree undefined

Q17. What is the order and degree of d^2y/dx^2 + x(dy/dx) + y = 0?

Order 2, Degree 1
Order 2, Degree 2
Order 1, Degree 1
Order 2, Degree undefined

Correct Answer: Order 2, Degree 1

Q18. Determine order and degree: (d^3y/dx^3) * (dy/dx) + y = 0.

Order 3, Degree 1
Order 3, Degree 2
Order 1, Degree 1
Order 3, Degree undefined

Correct Answer: Order 3, Degree 1

Q19. For the ODE d^2y/dx^2 = (dy/dx)^0, order and degree are:

Order 2, Degree 1
Order 2, Degree 0
Order 1, Degree 0
Order 2, Degree undefined

Correct Answer: Order 2, Degree 1

Q20. What are the order and degree of (d^2y/dx^2)^0 + y = 0?

Order 2, Degree 0
Order 2, Degree 1
Order 0, Degree 0
Order undefined, Degree undefined

Correct Answer: Order 2, Degree 0

Q21. Identify the order and degree: d^3y/dx^3 + (dy/dx)^{-1} = 0.

Order 3, Degree undefined
Order 3, Degree -1
Order 1, Degree undefined
Order 3, Degree 1

Correct Answer: Order 3, Degree undefined

Q22. For the equation y”” + (y”)^3 + y = 0, order and degree are:

Order 4, Degree 1
Order 4, Degree 3
Order 2, Degree 3
Order 4, Degree undefined

Correct Answer: Order 4, Degree 1

Q23. Determine order and degree: (d^2y/dx^2) + (d^2y/dx^2)^2 = 0.

Order 2, Degree 2
Order 2, Degree 1
Order 4, Degree 2
Order 2, Degree undefined

Correct Answer: Order 2, Degree 2

Q24. What is the order and degree of e^{y”} + y = 0?

Order 2, Degree undefined
Order 2, Degree 1
Order 1, Degree undefined
Order 2, Degree 0

Correct Answer: Order 2, Degree undefined

Q25. For the equation (d^2y/dx^2) + (d^3y/dx^3)^0 = 0, order and degree are:

Order 3, Degree 0
Order 3, Degree 1
Order 2, Degree 1
Order 2, Degree 0

Correct Answer: Order 3, Degree 0

Q26. Identify order and degree: (dy/dx) + (d^2y/dx^2) * (d^3y/dx^3) = 0.

Order 3, Degree 1
Order 3, Degree 2
Order 2, Degree 1
Order 3, Degree undefined

Correct Answer: Order 3, Degree 1

Q27. What is the order and degree of the differential equation (d^2y/dx^2)^2 + (d^3y/dx^3)^3 = 0?

Order 3, Degree 3
Order 3, Degree 2
Order 2, Degree 2
Order 3, Degree undefined

Correct Answer: Order 3, Degree 3

Q28. Determine order and degree: y + ln(d^2y/dx^2) = 0.

Order 2, Degree undefined
Order 2, Degree 1
Order 1, Degree undefined
Order 2, Degree 0

Correct Answer: Order 2, Degree undefined

Q29. For dy/dx = (y”)^2, identify order and degree.

Order 2, Degree 2
Order 1, Degree 2
Order 2, Degree 1
Order 1, Degree 1

Correct Answer: Order 2, Degree 2

Q30. What are the order and degree of the equation (d^4y/dx^4) + (d^2y/dx^2) = 0?

Order 4, Degree 1
Order 4, Degree 2
Order 2, Degree 1
Order 4, Degree undefined

Correct Answer: Order 4, Degree 1

Q31. Determine order and degree: (d^2y/dx^2) = sqrt(dy/dx).

Order 2, Degree undefined
Order 2, Degree 1/2
Order 2, Degree 1
Order 1, Degree undefined

Correct Answer: Order 2, Degree undefined

Q32. Identify the order and degree of (d^3y/dx^3) – 7 = 0.

Order 3, Degree 1
Order 3, Degree 0
Order 1, Degree 1
Order 3, Degree undefined

Correct Answer: Order 3, Degree 1

Q33. For the differential equation (y”)^5 + y = 0, the order and degree are:

Order 2, Degree 5
Order 2, Degree 1
Order 5, Degree 1
Order 2, Degree undefined

Correct Answer: Order 2, Degree 5

Q34. What are the order and degree of d^2y/dx^2 + (sin(dy/dx))^2 = 0?

Order 2, Degree undefined
Order 2, Degree 2
Order 1, Degree undefined
Order 2, Degree 1

Correct Answer: Order 2, Degree undefined

Q35. Determine order and degree: (d^2y/dx^2) + 1/(dy/dx) = 0.

Order 2, Degree undefined
Order 2, Degree -1
Order 1, Degree undefined
Order 2, Degree 1

Correct Answer: Order 2, Degree undefined

Q36. Identify order and degree: (d^3y/dx^3)^2 + (d^2y/dx^2)^3 = 0.

Order 3, Degree 2
Order 3, Degree 3
Order 2, Degree 3
Order 3, Degree undefined

Correct Answer: Order 3, Degree 2

Q37. For the ODE y’ + (y”)^0 = 0, what are order and degree?

Order 2, Degree 0
Order 2, Degree 1
Order 1, Degree 0
Order 1, Degree 1

Correct Answer: Order 2, Degree 0

Q38. What is the order and degree of d(dy/dx)/dx + y = 0?

Order 2, Degree 1
Order 1, Degree 1
Order 2, Degree 2
Order 1, Degree undefined

Correct Answer: Order 2, Degree 1

Q39. Determine the order and degree of (d^2y/dx^2) + (d^2y/dx^2)^{1/3} = 0.

Order 2, Degree undefined
Order 2, Degree 1/3
Order 2, Degree 1
Order 3, Degree undefined

Correct Answer: Order 2, Degree undefined

Q40. Identify order and degree: d^n y/dx^n + polynomial in lower derivatives = 0 (where n is a positive integer).

Order n, Degree 1
Order n, Degree n
Order n-1, Degree 1
Order n, Degree undefined

Correct Answer: Order n, Degree 1

Q41. For the ODE (d^2y/dx^2) = (x + y)^2, the order and degree are:

Order 2, Degree 1
Order 2, Degree 2
Order 1, Degree 1
Order 2, Degree undefined

Correct Answer: Order 2, Degree 1

Q42. What are the order and degree of the implicit equation F(x, y, y’) = 0 where highest derivative present is y’ (first derivative) and it appears polynomially?

Order 1, Degree equal to highest power of y’
Order 1, Degree 1 always
Order 0, Degree equal to highest power of y
Order 1, Degree undefined

Correct Answer: Order 1, Degree equal to highest power of y’

Q43. Identify order and degree: 3(d^4y/dx^4) + 2(d^3y/dx^3)^2 – 5 = 0.

Order 4, Degree 1
Order 4, Degree 2
Order 3, Degree 2
Order 4, Degree undefined

Correct Answer: Order 4, Degree 1

Q44. Determine order and degree: (d^2y/dx^2) + tan(dy/dx) = 0.

Order 2, Degree undefined
Order 2, Degree 1
Order 1, Degree undefined
Order 2, Degree 2

Correct Answer: Order 2, Degree undefined

Q45. For the equation (d^3y/dx^3) – (d^2y/dx^2)*(dy/dx) = 0, the order and degree are:

Order 3, Degree 1
Order 3, Degree 2
Order 2, Degree 1
Order 3, Degree undefined

Correct Answer: Order 3, Degree 1

Q46. What is the order and degree of (d^2y/dx^2) + (d^2y/dx^2)^{-2} = 0?

Order 2, Degree undefined
Order 2, Degree -2
Order 2, Degree 2
Order 2, Degree 1

Correct Answer: Order 2, Degree undefined

Q47. Identify the order and degree: y”’ + (y’)^4 + y = 0.

Order 3, Degree 1
Order 3, Degree 4
Order 1, Degree 4
Order 3, Degree undefined

Correct Answer: Order 3, Degree 1

Q48. Determine order and degree of the equation (d^2y/dx^2) = (d^3y/dx^3)^{1/2}.

Order 3, Degree undefined
Order 3, Degree 1/2
Order 2, Degree undefined
Order 3, Degree 1

Correct Answer: Order 3, Degree undefined

Q49. For the differential equation y” + (y’)^2 + y = 0, the order and degree are:

Order 2, Degree 2
Order 2, Degree 1
Order 1, Degree 2
Order 2, Degree undefined

Correct Answer: Order 2, Degree 2

Q50. What are the order and degree of the partial differential equation ∂^2u/∂x^2 + ∂u/∂t = 0 when considered as a PDE?

Order 2 (PDE), Degree 1 (in highest partial derivative)
Order 1 (PDE), Degree 1
Order 2 (ODE), Degree 1
Order undefined, Degree undefined

Correct Answer: Order 2 (PDE), Degree 1 (in highest partial derivative)

G S Sachin

I am a Registered Pharmacist under the Pharmacy Act, 1948, and the founder of PharmacyFreak.com. I hold a Bachelor of Pharmacy degree from Rungta College of Pharmaceutical Science and Research. With a strong academic foundation and practical knowledge, I am committed to providing accurate, easy-to-understand content to support pharmacy students and professionals. My aim is to make complex pharmaceutical concepts accessible and useful for real-world application.

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