JEE Main · Maths · Differential Equations

Linear Differential Equations: JEE Main previous year questions

Name: Linear Differential Equations: JEE Main previous year questions
Creator: Lumi

82 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 30 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 82; in 70 of 108 shifts
Years asked: 7/8; last asked 2026
Chance in a shift: 47%; calibrated model, how we compute it
Weighted estimate: 0.7; model; history: 0.6 a shift on average, typically 0.3–0.8

Key findings

01
Asked in 7 of 8 years with analysed shifts and in 70 of 108 shifts: 82 questions, #15 of 196 topics.
02
33% of its questions since 2020 tested an idea no earlier year had asked; 39 repeated an idea from the year before.
03
The most repeated idea is Integrating Factor Calculation, asked 22 times in 21 shifts (2020, 2021, 2022, 2023, 2024, 2025, 2026), most often as “solve initial value differential equation”.
04
JEE Main has asked 18 of the 61 ideas in this topic; 37 have never been asked, directly or inside another question.
05
Mostly asked as single correct (66%); 34% need a numerical answer, 0% are easy and 55% hard. It went up from 0.5 to 0.8 questions a shift since 2024.
06
The skill tested most is multi-step (83%), then calculation (16%).

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

Raw count: 2017: 0 in 1 shift · 2020: 3 in 12 shifts · 2021: 19 in 24 shifts · 2022: 21 in 24 shifts · 2023: 9 in 12 shifts · 2024: 17 in 18 shifts · 2025: 7 in 8 shifts · 2026: 6 in 9 shifts.

Up to 2023: 0.5; a shift, of 25
Since 2024: 0.8; +0.3
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 70/108; 65% of analysed shifts

Recent framings

solve initial value differential equation
numerical: solve linear differential equation
solve integral equation after functional equation

Revise first

Integrating Factor Calculation · asked 2020, 2021, 2022, 2023, 2024, 2025, 2026
Integrating Factors with Trigonometric Functions · asked 2022, 2024, 2025, 2026
Particular Solution Solving · asked 2021, 2022, 2024, 2026

How it is asked

Difficulty, format and skill

Across all 82 questions on Linear Differential Equations since 2017.

Difficulty

QUESTIONS

3745

Easy0 · 0%
Medium37 · 45%
Hard45 · 55%

Format

Single correct · 54 Q66%
Numerical value · 28 Q34%

Skill tested

Multi-step · 68 Q83%
Calculation · 13 Q16%
Conceptual · 1 Q1%

Repeats

New idea, or one asked before?

Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.

’17’20’21’22’23’24’25’26

Idea asked for the first time
Idea asked in an earlier year

Coverage of the topic

JEE Main has asked 18 of the 61 ideas in this topic. 37 have never been asked yet.

18637

Asked directly18 · 30%
Touched inside another question6 · 10%
Never asked37 · 61%

Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.

Drill down

Chapter, idea, question

Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.

chapterAskedShareYears’17’20’21’22’23’24’25’26

Open81 · 99%99%7/83192091776
18 ideas inside
- OpenRepeated22 · 27%27%7/823456
- OpenRepeated11 · 14%14%4/8352
- OpenRepeated7 · 9%9%4/8222
- OpenRepeated6 · 7%7%4/83
- OpenRepeated6 · 7%7%4/822
- OpenRepeated4 · 5%5%2/83
- OpenRepeated4 · 5%5%3/82
- OpenRepeated3 · 4%4%3/8
- OpenRepeated3 · 4%4%3/8
- OpenRepeated3 · 4%4%3/8
- OpenRepeated2 · 2%2%2/8
- OpenRepeated2 · 2%2%2/8
- OpenRepeated2 · 2%2%2/8
- OpenRepeated2 · 2%2%2/8
- Open1 · 1%1%1/8
- Open1 · 1%1%1/8
- Open1 · 1%1%1/8
- Open1 · 1%1%1/8
Open1 · 1%1%1/8

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

Every idea inside this topic

18 different ideas were tested; 14 came more than once.

Integrating Factor Calculation22×
solve initial value differential equation
Single correct · 21 shifts · 8 numerical
Particular Solution Solving11×
solve initial value differential equation
Single correct · 11 shifts · 4 numerical
Integrating Factors with Trigonometric Functions7×
solve initial value differential equation
Single correct · 7 shifts · 2 numerical
Generalized Substitution for LDEs6×
solve initial value differential equation
Single correct · 6 shifts · 2 numerical
Linear in x Form6×
solve initial value differential equation
Numerical value · 6 shifts · 3 numerical
Standard Linear Form Identification4×
solve initial value differential equation
Single correct · 4 shifts
Bernoulli Equation Reduction4×
solve initial value differential equation
Numerical value · 4 shifts · 2 numerical
Coefficient Normalization for Standard Form3×
solve initial value differential equation
Single correct · 3 shifts · 1 numerical
LDEs Formed via Leibniz Integral Rule3×
solve integral equation after functional equation
Single correct · 3 shifts
General Solution Formula3×
solve initial value differential equation
Single correct · 3 shifts · 1 numerical
Exact Differential Recognition in LDEs3×
solve initial value differential equation
Single correct · 3 shifts
LDEs Disguised in Exact Differential Form2×
solve initial value differential equation
Numerical value · 2 shifts · 1 numerical
Asymptotic Behavior of LDE Solutions2×
solve initial value differential equation
Numerical value · 2 shifts · 2 numerical
Forming LDEs from Geometric Conditions2×
solve differential equation from tangent-area condition
Numerical value · 2 shifts · 1 numerical
Analyzing Roots of LDE Solutions1×
number of intersections of solution curves
Single correct · 1 shift
Change of Independent Variable to form LDE1×
solve initial value differential equation
Single correct · 1 shift
Finding Extrema directly from LDE1×
nature of critical point from linear ode
Single correct · 1 shift
Inverse Trigonometric Integrating Factors1×
solve initial value differential equation
Numerical value · 1 shift · 1 numerical

Idea	Times	Shifts	Format	Numerical
Integrating Factor Calculationsolve initial value differential equation	22	21	Single correctMulti-step	8
Particular Solution Solvingsolve initial value differential equation	11	11	Single correctMulti-step	4
Integrating Factors with Trigonometric Functionssolve initial value differential equation	7	7	Single correctMulti-step	2
Generalized Substitution for LDEssolve initial value differential equation	6	6	Single correctMulti-step	2
Linear in x Formsolve initial value differential equation	6	6	Numerical valueMulti-step	3
Standard Linear Form Identificationsolve initial value differential equation	4	4	Single correctMulti-step	–
Bernoulli Equation Reductionsolve initial value differential equation	4	4	Numerical valueMulti-step	2
Coefficient Normalization for Standard Formsolve initial value differential equation	3	3	Single correctMulti-step	1
LDEs Formed via Leibniz Integral Rulesolve integral equation after functional equation	3	3	Single correctMulti-step	–
General Solution Formulasolve initial value differential equation	3	3	Single correctMulti-step	1
Exact Differential Recognition in LDEssolve initial value differential equation	3	3	Single correctMulti-step	–
LDEs Disguised in Exact Differential Formsolve initial value differential equation	2	2	Numerical valueMulti-step	1
Asymptotic Behavior of LDE Solutionssolve initial value differential equation	2	2	Numerical valueMulti-step	2
Forming LDEs from Geometric Conditionssolve differential equation from tangent-area condition	2	2	Numerical valueMulti-step	1
Analyzing Roots of LDE Solutionsnumber of intersections of solution curves	1	1	Single correctConceptual	–
Change of Independent Variable to form LDEsolve initial value differential equation	1	1	Single correctMulti-step	–
Finding Extrema directly from LDEnature of critical point from linear ode	1	1	Single correctMulti-step	–
Inverse Trigonometric Integrating Factorssolve initial value differential equation	1	1	Numerical valueMulti-step	1

Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas

Every question

Linear Differential Equations questions, year by year

The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.

Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.

Key findings

Questions a shift, year by year

Difficulty, format and skill

Difficulty

Format

Skill tested

New idea, or one asked before?

Coverage of the topic

Chapter, idea, question

Every idea inside this topic

Linear Differential Equations questions, year by year

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JEE Main 20257 questions in 7 shifts

JEE Main 202417 questions in 14 shifts

JEE Main 20239 questions in 8 shifts

JEE Main 202221 questions in 16 shifts

JEE Main 202119 questions in 16 shifts

JEE Main 20203 questions in 3 shifts

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