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Mathematics - Differential Equations

Practise 29 JEE Advanced previous year questions on Differential Equations, compiled from papers spanning 2007 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 Advanced tests.

Differential Equations has been asked in 18 of the 27 years of JEE Advanced papers analysed (2000–2026), with 29 questions in all. 31% of them were easy, 45% moderate and 24% tough. Most of its questions came from 2018, with 3 questions that year. In the last three years (2024–2026) it had 4 questions across 6 papers, about 0.7 per paper.

The chapter's 5 topics are not weighted equally: Linear Differential Equation (12 questions, 41%), Variable Separable Form (10 questions, 34%), and Homogeneous DE (3 questions, 10%) have been asked the most. Linear Differential Equation has also led over the last five years, with 4 questions. Linear Differential Equation has produced the most tough questions (3).

  1. 1Let be the solution of the differential equation , satisfying . Then the value of is2026 (Paper 2)Variable Separable Form
  2. 2Let be the real valued function defined on the interval , satisfying and the differential equation . Then which of the following statements 2026 (Paper 2)Linear Differential Equation
  3. 3For all , let , and be the functions satisfying respectively. Then is equal to _____2025 (Paper 1)Variable Separable Form
  4. 4Let be the solution of the differential equation satisfying . Then the value of is _____ .2025 (Paper 2)Homogeneous DE
  5. 5Let f : [ 1 . ) be a differentiable function such that f 1 = 1 3 and 3 1 x f t d t = x f x - x 3 3 , x [ 1 , ) . Let e denote the base of th2023 (Paper 2)Linear Differential Equation
  6. 6For x , let y x be a solution of the differential equation x 2 - 5 d y d x - 2 x y = - 2 x x 2 - 5 2 such that y 2 = 7 . Then the maximum va2023 (Paper 2)Linear Differential Equation
  7. 7If y x is the solution of the differential equation x d y - y 2 - 4 y d x = 0 for x 0 , y 1 = 2 , and the slope of the curve y = y x is neve2022 (Paper 2)Variable Separable Form
  8. 8For x , let the function y x be the solution of the differential equation d y d x + 12 y = cos 12 x , y 0 = 0 . Then, which of the following2022 (Paper 2)Linear Differential Equation
  9. 9For any real numbers and , let y , x , x R , be the solution of the differential equation d y d x + y = x e x , y 1 = 1 Let S = y , x : , R 2021 (Paper 2)Linear Differential Equation
  10. 10Let b be a nonzero real number. Suppose f : is a differentiable function such that f 0 = 1 . If the derivative f of f satisfies the equation2020 (Paper 2)Variable Separable Form
  11. 11Let T denote a curve y = y x which is in the first quadrant and let the point 1 , 0 lie on it. Let the tangent to T at a point P intersect t2019 (Paper 1)Variable Separable Form
  12. 12Let f : 0 , R be a continuous function such that f x = 1 - 2 x + 0 x e x - t f t d t for all x 0 , . Then, which of the following statement(2018 (Paper 1)Linear Differential Equation
  13. 13Let f : 0 , R be a twice differentiable function such that lim t x f x sin t - f t sin x t - x = sin 2 x for all x 0 , . If f 6 = - 12 , the2018 (Paper 2)Exact Forms
  14. 14Let f : be a differentiable function with f 0 = 0 . If y = f x satisfies the differential equation d y d x = 2 + 5 y 5 y - 2 , then the valu2018 (Paper 2)Variable Separable Form
  15. 15If y = y x satisfies the differential equation 8 x 9 + x d y = 4 + 9 + x - 1 d x and x 0 , y 0 = 7 , then y 256 =2017 (Paper 2)Variable Separable Form
  16. 16If f : R R is a differentiable function such that f x 2 f ( x ) for all x R and f 0 = 1 then2017 (Paper 2)Linear Differential Equation
  17. 17A solution curve of differential equation x 2 + x y + 4 x + 2 y + 4 d y d x - y 2 = 0 , x 0 passes through the point (1, 3). Then the soluti2016 (Paper 1)Exact Forms
  18. 18Let f : 0 , R be a differentiable function such that f x = 2 - f x x x ( 0 , ) and f 1 1 . Then,2016 (Paper 1)Linear Differential Equation
  19. 19Let y ( x ) be a solution of the differential equation 1 + e x y + y e x = 1 . If y 0 = 2 , then which of the following statements is (are) 2015 (Paper 1)Linear Differential Equation
  20. 20Consider the family of all circles whose centers lie on the straight line y = x . If this family of circles is represented by the differenti2015 (Paper 1)Formation of Differential Equation
  21. 21The function y = f x is the solution of the differential equation d y d x + x y x 2 - 1 = x 4 + 2 x 1 - x 2 in (- 1 , 1) satisfying f 0 = 0 2014 (Paper 2)Linear Differential Equation
  22. 22Let f : 0 , 2 R be a function which is continuous on 0 , 2 and is differentiable on 0 , 2 f 0 = 1 . Let F x = 0 x 2 f t d t for x 0 , 2 . If2014 (Paper 2)Variable Separable Form
  23. 23Let f : 1 2 1 R (the set of all real numbers) be a positive, non-constant and differentiable function such that f x 2 f x and f 1 2 = 1 . Th2013 (Paper 1)Formation of Differential Equation
  24. 24A curve passes through the point 1 , 6 . Let the slope of the curve at each point x , y be y x + sec y x , x 0 . Then the equation of the cu2013 (Paper 1)Homogeneous DE
  25. 25If satisfies the differential equation and , then2012 (Paper 1)Homogeneous DE
  26. 26Let , where denotes and is a given non-constant differentiable function on with . Then, the value of (2) is...2011 (Paper 2)Linear Differential Equation
  27. 27Let be a real-valued differentiable function on (the set of all real numbers) such that . If the -intercept of the tangent at any point on t2010 (Paper 1)Linear Differential Equation
  28. 28Let a solution of the differential equation satisfy Statement Statement is given by2008 (Paper 2)Variable Separable Form
  29. 29The differential equation determines a family of circles with2007 (Paper 2)Variable Separable Form

Frequently Asked Questions

1.How many questions are available for Differential Equations?

This chapter includes 29 questions compiled from JEE Advanced papers spanning 2007 to 2026.

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

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

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

Differential Equations has appeared in 18 of the 21 years of JEE Advanced papers covered here, with 29 questions across 20 papers - about one per paper it appears in.

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

Of the 29 questions analysed for this chapter, 31% are easy, 45% moderate and 24% tough. 2018 had the most, with 3 questions.

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

These topics have carried the most weightage in Differential Equations:

  • Linear Differential Equation - 12 questions (41%)
  • Variable Separable Form - 10 questions (34%)
  • Homogeneous DE - 3 questions (10%)
  • Linear Differential Equation has produced the most tough questions (3).
6.Is Differential Equations's weightage in JEE Advanced going up or down?

Across all 20 papers analysed, Differential Equations has averaged about 1.4 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.