Jump to a section

Mathematics - Differential Equations

Practise 58 WBJEE previous year questions on Differential Equations, compiled from papers spanning 2009 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 WBJEE tests.

Differential Equations has been asked in 18 of the 18 years of WBJEE papers analysed (2009–2026), with 58 questions in all. 34% of them were easy, 52% moderate and 14% tough. Most of its questions came from 2014, with 6 questions that year. In the last three years (2024–2026) it had 8 questions across 3 papers, about 2.7 per paper.

The chapter's 7 topics are not weighted equally: Linear Differential Equation (17 questions, 29%), Variable Separable Form (14 questions, 24%), and Formation of Differential Equation (12 questions, 21%) have been asked the most. Over the last five years the most frequent topics have been Variable Separable Form (5), Linear Differential Equation (3), and Formation of Differential Equation (3). Linear Differential Equation has produced the most tough questions (7).

  1. 1If , where ; then the number of solutions of the equation in is/are (where represents fractional part function)2026Linear Differential Equation
  2. 2The solution of the differential equation , given is2026Variable Separable Form
  3. 3Let be a differentiable function such that and . Suppose for all , . Then the value of belongs to2026Variable Separable Form
  4. 4If and , then is equal to2025Variable Separable Form
  5. 5The population at time of a certain mouse species follows the differential equation . If , then the time at which the population becomes zer2025Variable Separable Form
  6. 6If denote the derivative of are constants , then , holds for2024Linear Differential Equation
  7. 7If , then is2024Exact Forms
  8. 8Let be a differential function with . If then2024Linear Differential Equation
  9. 9If \(y= {x}{ _e|c x|}\) is the solution of the differential equation \( {d y}{d x}= {y}{x}+ ( {x}{y} )\), then \( ( {x}{y} )\) is given by2023Formation of Differential Equation
  10. 10If \(x= \) and \(y= k \), then \( (1-x^2 ) y_2-x y_1- y=0\), for \( =\)2023Formation of Differential Equation
  11. 11The family of curves \(y=e^{a x}\), where ' \(a\) ' is arbitrary constant, is represented by the differential equation2023Formation of Differential Equation
  12. 12If , then is equal to2022Exact Forms
  13. 13The solution of is (C is arbitrary real constant) where is equal to2022Variable Separable Form
  14. 14If , then is equal to2021Variable Separable Form
  15. 15The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is2021Formation of Differential Equation
  16. 16Let be a differentiable function with If , then where2020Applications of DE
  17. 17If and then the value of is2020Homogeneous DE
  18. 18The differential equation of the family of curves where are arbitrary constants is2020Formation of Differential Equation
  19. 19Let , Then2020Formation of Differential Equation
  20. 20The general solution of the differential equation is is an arbitrary constant2019Homogeneous DE
  21. 21General solution of is is an arbitrary constant)2019Variable Separable Form
  22. 22The differential equation representing the family of curves where is a parameter, is of2018Order and Degree
  23. 23Let be a solution of and Then y(1) s equal to2018Linear Differential Equation
  24. 24Solution of ('a' being a constant) is2017Variable Separable Form
  25. 25The integrating factor of the first order differential equation is2017Linear Differential Equation
  26. 26If the solution of the differential equation be then is equal to2016Linear Differential Equation
  27. 27The order of the differential equation of all parabolas whose axis of symmetry along -axis is2016Order and Degree
  28. 28General solution of is (Here, is an arbitrary constant)2016Variable Separable Form
  29. 29The integrating factor of the differential equation is2015Linear Differential Equation
  30. 30If , then which of the following differential equation is satisfied?2015Formation of Differential Equation
  31. 31If and are solutions of the differential equation where and are real constants, then which of the following is/are always true?2015Formation of Differential Equation
  32. 32The integrating factor of the differential equation is2014Linear Differential Equation
  33. 33If , then it satisfies the differential equation where is equal to2014Applications of DE
  34. 34The solution of the differential equation is (where, is a constant)2014Linear Differential Equation
  35. 35The curve satisfies the differential equation2014Formation of Differential Equation
  36. 36The solution of the differential equation under the condition when is2014Linear Differential Equation
  37. 37If and are two independent solutions of the differential equation then additional solution(s) of the given differential equation is(are)2014Formation of Differential Equation
  38. 38The solution of the differential equation satisfies . Then the solution is2013Linear Differential Equation
  39. 39The general solution of the differential equation is2012Homogeneous DE
  40. 40The integrating factor of the differential equation is given by2012Linear Differential Equation
  41. 41The solution of , is2012Homogeneous DE
  42. 42Let be the solution of the differential equation satisfying Then, satisfies2012Applications of DE
  43. 43The general solution of the differential equation \( {d^2 y}{d x^2}+8 {d y}{d x}+16 y=0\) is2011Linear Differential Equation
  44. 44The degree and order of the differential equation \(y=x ( {d y}{d x} )^2+ {d y}{d x}\) are respectively2011Order and Degree
  45. 45The general solution of the differential equation \( _{ {e}} ( {d y}{d x} )=x+y\) is2011Variable Separable Form
  46. 46The solution of \( {d y}{d x}= {y}{x}+ {y}{x}\) is2011Homogeneous DE
  47. 47Integrating Factor (I.F.) of the defferential equation \( {d y}{d x}- {3 x^2 y}{1+x^3}= { ^2(x)}{1+x} { is }\)2011Linear Differential Equation
  48. 48The differential equation of \( {y}= {ae}^{ {bx}}\) (a & \( {b}\) are parameters) is2011Formation of Differential Equation
  49. 49The general solution of the different equation is2010Linear Differential Equation
  50. 50If where , then the value of at is2010Linear Differential Equation

Frequently Asked Questions

1.How many questions are available for Differential Equations?

This chapter includes 58 questions compiled from WBJEE papers spanning 2009 to 2026.

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

These are WBJEE 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 WBJEE Mathematics?

Differential Equations has appeared in 18 of the 18 years of WBJEE papers covered here, with 58 questions across 18 papers - about 3 per paper it appears in.

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

Of the 58 questions analysed for this chapter, 34% are easy, 52% moderate and 14% tough. 2014 had the most, with 6 questions.

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

These topics have carried the most weightage in Differential Equations:

  • Linear Differential Equation - 17 questions (29%)
  • Variable Separable Form - 14 questions (24%)
  • Formation of Differential Equation - 12 questions (21%)
  • Linear Differential Equation has produced the most tough questions (7).
6.Is Differential Equations's weightage in WBJEE going up or down?

Across all 18 papers analysed, Differential Equations has averaged about 3.2 questions per paper. In the last three years (2024–2026), that average has fallen, at about 2.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.