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Mathematics - Differential Equations

Practise 257 JEE Main previous year questions on Differential Equations, compiled from papers spanning 2002 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Differential Equations has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 257 questions in all. 18% of them were easy, 53% moderate and 28% tough. Most of its questions came from 2021, with 42 questions that year. In the last three years (2024–2026) it had 66 questions across 49 papers, about 1.3 per paper.

The chapter's 7 topics are not weighted equally: Linear Differential Equation (130 questions, 51%), Variable Separable Form (46 questions, 18%), and Homogeneous DE (27 questions, 11%) have been asked the most. Linear Differential Equation has also led over the last five years, with 81 questions. Linear Differential Equation has produced the most tough questions (40).

  1. 1Let be the solution of the differential equation , , . Then equals:08 Apr, 2026 (E)Linear Differential Equation
  2. 2Let be the solution of the differential equation , . If , then the greatest integer less than is _______.06 Apr, 2026 (M)Variable Separable Form
  3. 3Let be the solution of the differential equation , and let . Then the number of integral values of , for which the equation represents a cir05 Apr, 2026 (M)Homogeneous DE
  4. 4Let be the solution of the differential equation , , . If , then equals _______.05 Apr, 2026 (E)Linear Differential Equation
  5. 5Let be the solution of the differential equation , . Then is equal to:04 Apr, 2026 (M)Variable Separable Form
  6. 6Let be the solution of the differential equation: , , satisfying . If , then is equal to:04 Apr, 2026 (E)Linear Differential Equation
  7. 7If the curve passes through the point and satisfies the differential equation , , then is equal to :02 Apr, 2026 (M)Variable Separable Form
  8. 8Let be the solution curve of the differential equation , . If the curve passes through the point , then a value of is :02 Apr, 2026 (M)Variable Separable Form
  9. 9Let be the solution of the differential equation , , . Then is equal to:02 Apr, 2026 (E)Homogeneous DE
  10. 10Let be the solution of the differential equation . If , then is equal to28 Jan, 2026 (M)Linear Differential Equation
  11. 11Let be the solution of the differential equation . If , then is equal to :28 Jan, 2026 (E)Linear Differential Equation
  12. 12Let be a differentiable function in the interval such that , and for each . Then is equal to24 Jan, 2026 (E)Linear Differential Equation
  13. 13Let be the solution of the differential equation . Then is equal to :23 Jan, 2026 (M)Linear Differential Equation
  14. 14Let be a twice differentiable non-negative function such that . Then the mean of is equal to .23 Jan, 2026 (M)Variable Separable Form
  15. 15If the solution curve of the differential equation , passes through the point , then the local maximum value of is .23 Jan, 2026 (E)Linear Differential Equation
  16. 16Let the solution curve of the differential equation , , be . Then is equal to22 Jan, 2026 (M)Homogeneous DE
  17. 17Let be a differentiable function. If for all , then the value of is22 Jan, 2026 (M)Linear Differential Equation
  18. 18If satisfies the differential equation and , then is equal to :22 Jan, 2026 (E)Variable Separable Form
  19. 19Let be the solution curve of the differential equation . Then the value of is :21 Jan, 2026 (M)Linear Differential Equation
  20. 20Let be the solution of the differential equation , . Then is equal to :21 Jan, 2026 (E)Linear Differential Equation
  21. 21Let and for . If , then is :-08 Apr, 2025 (E)Linear Differential Equation
  22. 22Let be the solution curve of the differential equation passing through the point . Then is equal to :07 Apr, 2025 (M)Linear Differential Equation
  23. 23Let be the solution of the differential equation , . Then is :07 Apr, 2025 (E)Linear Differential Equation
  24. 24Let be differentiable function such that for all . Then the area of the region bounded by and the coordinate axes is04 Apr, 2025 (M)Linear Differential Equation
  25. 25If a curve passes through the point and satisfies the differential equation , then at , the value of cosy is:04 Apr, 2025 (E)Linear Differential Equation
  26. 26Let be a differentiable function such that and let satisfy the differential equation . If , then is equal to03 Apr, 2025 (M)Linear Differential Equation
  27. 27Let be the solution of the differential equation . Then is equal to03 Apr, 2025 (E)Linear Differential Equation
  28. 28Let be a thrice differentiable odd function satisfying . Then is equal to _______.02 Apr, 2025 (M)Variable Separable Form
  29. 29Let be a differentiable function, If for all , then the value of is :02 Apr, 2025 (E)Linear Differential Equation
  30. 30Let be the solution of the differential equation such that . Then is equal to _______.02 Apr, 2025 (E)Linear Differential Equation
  31. 31Let \(y=y(x)\) be the solution of the differential equation \( x ( _{ {e}}( x) )^2 {dy}+ ( x-3 y x _{ {e}}( x) ) {d} x=0, x (0, { }{2} )\). 29 Jan, 2025 (M)Linear Differential Equation
  32. 32If for the solution curve of the differential equation , , then is equal to :29 Jan, 2025 (E)Linear Differential Equation
  33. 33If is the solution of the differential equation, , then is equal to28 Jan, 2025 (E)Linear Differential Equation
  34. 34Let be the solution of the differential equation . Then is equal to24 Jan, 2025 (M)Linear Differential Equation
  35. 35Let be a differentiable function such that . Then is equal to ______.24 Jan, 2025 (M)Linear Differential Equation
  36. 36Let be a function which is differentiable at all points of its domain and satisfies the condition , with . Then is equal to :24 Jan, 2025 (E)Linear Differential Equation
  37. 37Let be the solution of the differential equation . If , then is equal to ________.24 Jan, 2025 (E)Linear Differential Equation
  38. 38Let a curve pass through the points and . If the curve satisfies the differential equation , then is equal to23 Jan, 2025 (M)Linear Differential Equation
  39. 39Let be the solution of the differential equation and . Then is equal to :23 Jan, 2025 (E)Homogeneous DE
  40. 40Let be the solution of the differential equation . If , then is :22 Jan, 2025 (M)Linear Differential Equation
  41. 41If is the solution of the differential equation with , then is equal to :22 Jan, 2025 (E)Linear Differential Equation
  42. 42Let be the solution of the differential equation such that . If then is equal to _______ .22 Jan, 2025 (E)Linear Differential Equation
  43. 43The solution curve, of the differential equation , passing through the point is a conic, whose vertex lies on the line:09 Apr, 2024 (M)Homogeneous DE
  44. 44The solution of the differential equation , is :09 Apr, 2024 (M)Variable Separable Form
  45. 45Let be the solution of the differential equation . Then is equal to08 Apr, 2024 (M)Variable Separable Form
  46. 46Let be the solution curve of the differential equation . Then is equal to :08 Apr, 2024 (E)Linear Differential Equation
  47. 47Let be the solution of the differential equation , . Then is equal to ________08 Apr, 2024 (E)Exact Forms
  48. 48Let be the solution of the differential equation , . Then is06 Apr, 2024 (M)Linear Differential Equation
  49. 49Let be the solution of the differential equation and . Then, is equal to06 Apr, 2024 (M)Linear Differential Equation
  50. 50Suppose the solution of the differential equation represents a circle passing through origin. Then the radius of this circle is :06 Apr, 2024 (E)Exact Forms

Frequently Asked Questions

1.How many questions are available for Differential Equations?

This chapter includes 257 questions compiled from JEE Main papers spanning 2002 to 2026.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Differential Equations chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Differential Equations an important chapter for JEE Main Mathematics?

Differential Equations has appeared in 25 of the 25 years of JEE Main papers covered here, with 257 questions across 189 papers - about one per paper it appears in.

4.What is the difficulty level of Differential Equations questions in JEE Main?

Of the 257 questions analysed for this chapter, 18% are easy, 53% moderate and 28% tough. 2021 had the most, with 42 questions.

5.Which topics in Differential Equations should I focus on?

These topics have carried the most weightage in Differential Equations:

  • Linear Differential Equation - 130 questions (51%)
  • Variable Separable Form - 46 questions (18%)
  • Homogeneous DE - 27 questions (11%)
  • Linear Differential Equation has produced the most tough questions (40).
6.Is Differential Equations's weightage in JEE Main going up or down?

Across all 189 papers analysed, Differential Equations has averaged about 1.4 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.