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JEE Main Differential Equations questions with solutions

Order, degree and solution of first-order differential equations. 9 questions from our 2017–2025 JEE Main pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Differential Equations for JEE Advanced · Differential Equations for NDA

JEE Main 2025

If y(x) satisfies dy/dx+ytan x=sin 2x with y(0)=1, then y ((π)/(3)) equalsJEE Main 2025 · hard

JEE Main 2024

Given y(1)=1, the solution of dy/dx+y/x=x^2, evaluated at x=2, isJEE Main 2024 · medium
The curve y=y(x) satisfies (x^2+y^2 dx=2xy dy for x>0 and passes through (2,1). The value of [y(4)]^2 isJEE Main 2024 · hard

JEE Main 2023

Let y(x) satisfy dy/dx=y+y^2e^x with y(0)=1. Then y(-ln 2) equalsJEE Main 2023 · hard

JEE Main 2022

If y(x) satisfies x dy/dx+y=x^3 and y(1)=1, then the value of y(2) isJEE Main 2022 · medium

JEE Main 2021

The solution of dy/dx+ytan x=sec x with y(0)=2 gives y ((π)/(4))=JEE Main 2021 · hard

JEE Main 2019

If y=y(x) satisfies dy/dx=y/x+tan y/x for x>0 with y(1)=(π)/(6), then y(√2) equalsJEE Main 2019 · medium
If y=y(x) solves x dy/dx=x+y for x>0 with y(1)=2, then y(e) isJEE Main 2019 · hard

JEE Main 2017

The order and degree of the differential equation [1+(dy/dx)^2]^3/2=(d^2y)/(dx^2 are respectivelyJEE Main 2017 · medium

Other Mathematics topics

Area Under Curves 7 Binomial Theorem 12 Complex Numbers 10 Conic Sections 5 Differentiation and Application of Derivatives 19 Indefinite and Definite Integrals 16 Limits 9 Matrices and Determinants 19 Permutations and Combinations 10 Probability 9 Quadratic Equations 9 Sequences and Series 9 Sets, Relations and Functions 10 Statistics 6 Straight Lines and Circles 9 Three Dimensional Geometry 14 Trigonometry and Inverse Trigonometric Functions 9 Vector Algebra 8