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Mathematics - Differential Equations

Practise 105 NTA Abhyas (JEE Main) questions on Differential Equations. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Differential Equations has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 105 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1The curve satisfying the differential equation sin x 3 e y d y + 3 x 2 cos x 3 e y d x = x sin x 2 d x (where, C is the constant of integrat
  2. 2The general solution of the differential equation d y d x = 2 y tan ⁡ x + tan 2 ⁡ x , ∀ x ∈ 0 , π 2 is yf x = x 2 - sin ⁡ 2 x 4 + C , (where
  3. 3The solution of the differential equation d y d x = x - y x + 4 y is (where C is the constant of integration)
  4. 4The equation of the curve for which the slope of the tangent at any point is given by x + y + 1 d y d x = 1 is (where, c is an arbitrary con
  5. 5If the order of the differential equation of the family of circles touching the x -axis at the origin is k , then 2 k is equal to
  6. 6Let f [ 1 , ∞ ) → [ 2 , ∞ ) be a differentiable function such that f ( 1 ) = 1 3 . If 6 ∫ 1 x f t dt = 3 x f x - x 3 for all x ≥ 1 , then th
  7. 7The solution of the differential equation x d x + y d y = x d y - y d x x 2 + y 2 is tan f x , y - C = y x (where, C is an arbitrary constan
  8. 8The solution of the differential equation d y d x = x y + y x y + x is y - x = ln x y + C (where, C is an arbitrary constant and x , y 0 ).
  9. 9The solution of the differential equation x d x + y sin 2 x d y = y d y + x sin 2 y d x is (where, c is an arbitrary constant)
  10. 10The solution of the differential equation d y d x + x y ln ⁡ y = x 3 y is equal to (where, C is the constant of integration)
  11. 11The solution of the differential equation y d x - x d y x y = x d x + y d y is (where, C is an arbitrary constant)
  12. 12The solution of the differential equation 3 sin 2 x cos x y 2 d x + 2 y sin 3 x d y = sin x d x is (where, C is an arbitrary constant)
  13. 13The order of the differential equation whose general solution is given by y = c 1 + c 2 cos x + c 3 - c 4 e x + c 5 where c 1 , c 2 , c 3 ,
  14. 14The order of the differential equation of the family of parabolas symmetric about y = 1 and tangent to x = 2 is
  15. 15The differential equation of the family of ellipses having centres along the line y = 4 and major and minor axes parallel to the coordinate
  16. 16The solution of the differential equation y 2 x 4 + y d y + 4 x y 2 - 1 x 2 d x = 0 is (where C is an arbitrary constant)
  17. 17If the general solution of the differential equation y ' = y x + ϕ x y , for some function ϕ , is given by yln | c x | = x , where c is an a
  18. 18The solution of the differential equation d y d x = x - y x - 3 y is (where, c is an arbitrary constant)
  19. 19If the solution of the differential equation 1 + e x y d x + e x y 1 - x y d y = 0 is x + k y e x y = C (where, C is an arbitrary constant),
  20. 20The equation of the curve satisfying the differential equation x e x sin ⁡ y d y - x + 1 e x cos ⁡ y d x = y d y and passing through the ori
  21. 21The order of the differential equation of the family of circles touching the y -axis at the origin is k , then the maximum value of y = k co
  22. 22The curve passing through P 2 , 7 2 and having slope 1 - 1 x 2 at P x , y also passes through
  23. 23The solution of the differential equation x c o s y d y d x + sin ⁡ y = 1 is (Here, x 0 and λ is an arbitrary constant)
  24. 24The solution of d y = cos x 2 - y c o s e c x d x , where y = 2 when x = π / 4 , is
  25. 25The solution of the differential equation d y d x = a x + b , a ≠ 0 represents
  26. 26The solution of the differential equation xdy = tan y + e 1 / x 2 x sec y dx is (where C is the constant of integration)
  27. 27The solution of the differential equation d y d x + x 2 x + y = x 3 2 x + y 3 - 2 is ( C being an arbitrary constant)
  28. 28The straight line y = 2 x meets y = f x at P , where f x is a solution of the differential equation d y d x = x 2 + x y x 2 + y 2 such that
  29. 29The general solution of the differential equation 2 x y – x d y + y d x = 0 is (Here x, y 0)
  30. 30The order of the differential equation of the family of curves y = a 3 b x + c + d s i n x + e is (where, a , b , c , d , e are arbitrary co
  31. 31The general solution of the differential equation d y d x + sin x + y 2 = sin x - y 2 is (where c is an arbitrary constant)
  32. 32The population p ( t ) at a time t of a certain mouse species satisfies the differential equation dp t dt = 0.5 p ( t ) - 450 . If p ( 0 ) =
  33. 33The curve having differential equation, x cos ⁡ y d y d x + sin ⁡ y = x and passing through the origin, also passes through
  34. 34The solution of the differential equation x d y d x = y ln y 2 x 2 is (where, c is an arbitrary constant)
  35. 35The slope of normal at any point P of a curve (lying in the first quadrant) is reciprocal of twice the product of the abscissa and the ordin
  36. 36The solution of the differential equation 1 x 2 d y d x + x y = x x 3 y 1 2 , x 1 is 9 y = f x + c 1 x 2 1 4 , where c is an arbitrary const
  37. 37The curve passing through P π 2 , π is such that for a tangent drawn to it at a point Q , the ratio of the y -intercept and the ordinate of
  38. 38The solution of the differential equation d y d x + x y 1 − x 2 = x y , x 1 is y = - f x 3 + C 1 - x 2 1 4 , where f 1 2 = 3 4 and C is an a
  39. 39The solution of the differential equation 2 y d x + x d y = 2 x y d x is (where, C is an arbitrary constant)
  40. 40The solution of the differential equation d x d y = x 2 e y - x ∀ x 0 is λ x + 2 c x 2 e y = e y (where, c is an arbitrary constant). Then,
  41. 41The solution of the differential equation x d y - y d x + 3 x 2 y 2 e x 3 d x = 0 is (where, c is an arbitrary constant)
  42. 42If the straight line y = x meets y = f ( x ) at P , where f x is a solution of the differential equation d y d x = x 2 + x y x 2 + y 2 such
  43. 43If the solution of the differential equation x 2 d y + 2 x y d x = sin x d x is x k y + cos x = C (where C is an arbitrary constant), then t
  44. 44A curve in the first quadrant is such that the slope of O P is twice the slope of the tangent drawn at P to the curve, where O is the origin
  45. 45The solution of the differential equation y cos x . d x = sin x . d y + x y 2 d x is (where, c is an arbitrary constant)
  46. 46The solution of the differential equation y sin 2 x d y + sin x cos x y 2 d x = x d x is (where C is the constant of integration)
  47. 47The solution of the differential equation cos ⁡ x d y d x + y sin ⁡ x = 1 is (where, c is an arbitrary constant)
  48. 48If y = f x satisfies the differential equation d y d x + 2 x 1 + x 2 y = 3 x 2 1 + x 2 where f 1 = 1 , then f 2 is equal to
  49. 49The equation of the curve passing through the point 1,1 and satisfying the differential equation d y d x = x + 2 y - 3 y - 2 x + 1 is
  50. 50The differential equation of the family of curves whose tangent at any point makes an angle of π 4 with the ellipse x 2 4 + y 2 = 1 is

Frequently Asked Questions

1.How many questions are available for Differential Equations?

This chapter includes 105 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Differential Equations questions in NTA Abhyas (JEE Main)?

Of the 105 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

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

All of this chapter's questions come from a single topic: Uncategorized.