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Mathematics - Differential Equations

Practise 49 KCET 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 KCET tests.

Differential Equations has been asked in 20 of the 20 years of KCET papers analysed (2007–2026), with 49 questions in all. 45% of them were easy, 45% moderate and 10% tough. Most of its questions came from 2026, with 4 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: Order and Degree (14 questions, 29%), Linear Differential Equation (13 questions, 27%), and Variable Separable Form (8 questions, 16%) have been asked the most. Order and Degree has also led over the last five years, with 4 questions. Linear Differential Equation has produced the most tough questions (1).

  1. 1Integrating factor of the differential equation is2026Linear Differential Equation
  2. 2If and , then2026Variable Separable Form
  3. 3, then is equal to2026Variable Separable Form
  4. 4Sum of the squares of the order and degree (if defined) of a differential equation is2026Order and Degree
  5. 5General solution of the differential equation is2025Linear Differential Equation
  6. 6If ' ' and ' ' are the order and degree respectively of the differentiable equation. , then2025Order and Degree
  7. 7The solution of is2024Variable Separable Form
  8. 8The family of curves whose and intercepts of a tangent at any point are respectively double the and coordinates of that point is2024Applications of DE
  9. 9If , then is a2023Formation of Differential Equation
  10. 10If a curve passes through the point and at any point on the curve, the product of the slope of its tangent and coordinate of the point is eq2023Formation of Differential Equation
  11. 11The degree of the differential equation is2023Order and Degree
  12. 12If , then2022Linear Differential Equation
  13. 13The solution of the differential equation is2022Variable Separable Form
  14. 14If is the solution of differential equation is equal to2022Linear Differential Equation
  15. 15The sum of the degree and order of the differential equation is2022Order and Degree
  16. 16Solution of differential equating represents2021Homogeneous DE
  17. 17The number of solutions of , when is2021Linear Differential Equation
  18. 18Find the value of is2020Order and Degree
  19. 19The area of the region bounded by the curve and the line is2020Homogeneous DE
  20. 20The order of the differential equation \( y=c_{1} e^{c_{2}+x}+c_{3} e^{c_{4}+x} \) is2019Order and Degree
  21. 21The integrating factor of the differential equation \( (2 x+3 y^{2} ) d y=y d x(y>0) \) is2019Linear Differential Equation
  22. 22The degree and the order of the differential equation \( {d^{2} y}{d x^{2}}= [3]{ (1+ ( {d y}{d x} )^{2} )} \) respectively are2018Order and Degree
  23. 23The solution of the differential equation \( x {d y}{d x}-y=3 \) represents a family of2018Homogeneous DE
  24. 24The integrating factor of \( {d y}{d x}+y= {1+y}{x} \) is2018Linear Differential Equation
  25. 25If \( A= {1}{ } [ {array}{ll} ^{-1}( x) & ^{-1} ( {x}{I I} ) \\ ^{-1} ( {x}{I I} ) & ^{-1}( x) {array} ] \) then \( A-B \) is2017Linear Differential Equation
  26. 26If \( {A} \) is a square matrix of order \( 3 3 \), then \( | {KA}| \) is equal to2017Order and Degree
  27. 27The degree of the differential equation \( [1+ ( {d y}{d x} )^{2} ]^{2}= {d^{2} y}{d x^{2}} \) is2017Linear Differential Equation
  28. 28The solution for the differential equation \( {d y}{y}+ {d x}{x}=0 \)2016Variable Separable Form
  29. 29The order and degree of the differential equation \( [1+ ( {d y}{d x} )^{2}+ ( {d y}{d x} ) ]^{ {3}{4}}= {d^{2} y}{d x^{2}} \)2016Order and Degree
  30. 30Integrating factor of \( x {d y}{d x}-y=x^{4}-3 x \) is2016Linear Differential Equation
  31. 31\[ f(x)= {1}{2}- ( { x}{2} )-1 Find domain of \( (f+g) \)2015Order and Degree
  32. 32Write the set builder form \( A=\{-1,1\}: \)2015Linear Differential Equation
  33. 33Let \( f: N N \) defined by \( f(n)= \{ {array}{cl} {n+1}{2} ; & { if } n { is odd } \\ {n}{2} ; & { if } n { is even } {array} . \) then \(2014Formation of Differential Equation
  34. 34If \( {a} \) and \( {b} \) are two unit vectors inclined at an angle \( { }{3} \), then the value of \( | {a}+ {b}| \) is2014Order and Degree
  35. 35The value of \( [ {a}- {b} {b}- {c} {c}- {a}] \) is equal to2014Linear Differential Equation
  36. 36The general solution of the differential equation is2013Exact Forms
  37. 37If and are order and degree of the differential equation , then2013Order and Degree
  38. 38If is a function such that and and , then is equal to2013Variable Separable Form
  39. 39If and , then is equal to2013Exact Forms
  40. 40If , then is equal to2012Formation of Differential Equation
  41. 41Solution of when and is2012Variable Separable Form
  42. 42If , then2011Formation of Differential Equation
  43. 43The general solution of is2011Variable Separable Form
  44. 44The order and degree of the differential equation where (here and are arbitrary constants) respectively are2010Order and Degree
  45. 45The general solution of the differential equation is a family of2010Linear Differential Equation
  46. 46The differential equation of the family of circles passing through the orign and having their centres on the -axis is2009Formation of Differential Equation
  47. 47The differential equation crepresents2008Applications of DE
  48. 48The differential equation of the family of straight lines whose slope is equal to -intercept is2007Formation of Differential Equation
  49. 49The order and degree of the differential equation are respectively2007Order and Degree

Frequently Asked Questions

1.How many questions are available for Differential Equations?

This chapter includes 49 questions compiled from KCET papers spanning 2007 to 2026.

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

These are KCET 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 KCET Mathematics?

Differential Equations has appeared in 20 of the 20 years of KCET papers covered here, with 49 questions across 20 papers - about 2 per paper it appears in.

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

Of the 49 questions analysed for this chapter, 45% are easy, 45% moderate and 10% tough. 2026 had the most, with 4 questions.

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

These topics have carried the most weightage in Differential Equations:

  • Order and Degree - 14 questions (29%)
  • Linear Differential Equation - 13 questions (27%)
  • Variable Separable Form - 8 questions (16%)
  • Linear Differential Equation has produced the most tough questions (1).
6.Is Differential Equations's weightage in KCET going up or down?

Across all 20 papers analysed, Differential Equations has averaged about 2.5 questions per paper. In the last three years (2024–2026), that average has stayed about the same, 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.