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JEE Advanced Differential Equations questions with solutions

Order, degree and solution of first-order differential equations. 20 questions from our 2016–2025 JEE Advanced pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

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

JEE Advanced 2025

Let y=y(x) satisfy (1+x^2dy/dx+2xy=3x^2 with y(0)=1. Find ∫0^1y(x) dx.JEE Advanced 2025 Paper 1 · medium
The curve y=y(x), x>0, y>0, passes through (1,√3) and satisfies dy/dx=(x^2+y^2/(2xy).JEE Advanced 2025 Paper 2 · medium

JEE Advanced 2024

A curve y=y(x) for x>0 passes through (1,3). For every point P(x,y) on it, the tangent at P meets the y-axis at Q, and the midpoint of PQ lies on the…JEE Advanced 2024 Paper 1 · medium
Let f:(0,∞)→mathbbR be the differentiable function satisfying x f'(x)+2f(x)=x^2 for all x>0 and f(1)=1.JEE Advanced 2024 Paper 2 · medium

JEE Advanced 2023

Let y=y(x) be the solution of 2xy dy/dx=x^2+y^2 for x>0 with y(1)=2 and y>0. The slope of the tangent to the curve at the point where x=3 isJEE Advanced 2023 Paper 1 · medium
Let f:mathbb R→mathbb R be a differentiable function satisfying x f'(x)-f(x)=x^2e^x for all real x, and f(1)=e.JEE Advanced 2023 Paper 2 · medium

JEE Advanced 2022

A curve y=f(x), x>0, passes through (1,1) and has the property that at every point P(x,y) on it the tangent cuts the y-axis at a point whose ordinate…JEE Advanced 2022 Paper 2 · hard

JEE Advanced 2021

Paragraph 1: A curve y=f(x), x>0, passes through the point (1,3). For every point P(x,y) on the curve, the tangent at P meets the y-axis at a point…JEE Advanced 2021 Paper 1 · 2-question set
Paragraph 1: A differentiable function f:(0,∞)→mathbb R satisfies the differential equation x f'(x)-2f(x)=x^3e^x for all x>0, together with the…JEE Advanced 2021 Paper 2 · 2-question set

JEE Advanced 2020

Let y=y(x), x>0, be the solution of xdy/dx+2y=x^2 with y(1)=1.JEE Advanced 2020 Paper 1 · medium
Let y=y(x) with y>0 be the solution of (x^2+y^2 dx=2xy dy for x>0 passing through the point (2,√2).JEE Advanced 2020 Paper 2 · medium
Let y=y(x) be the solution of dy/dx+ytan x=sin 2x on (-(π)/(2),(π)/(2)) with y(0)=1. Find y ((π)/(4)).JEE Advanced 2020 Paper 2 · medium

JEE Advanced 2019

A curve passes through (1,0) and satisfies xdy/dx=y+√(x^2+y^2 for x>0. Which of the following statements is correct?JEE Advanced 2019 Paper 2 · medium

JEE Advanced 2018

Let y=f(x) be the solution of dy/dx=y/x+(y^2/(x^2 on (1,e) with f(1)=1. Find the value of f(√ e)+f'(√ e).JEE Advanced 2018 Paper 1 · medium
Let y=y(x) be the solution of dy/dx+ytan x=sin 2x on [0,(π)/(2)) with y(0)=1.JEE Advanced 2018 Paper 2 · hard

JEE Advanced 2017

Let y=y(x) be the solution of xdy/dx+y=x^2y^2 with y(1)=1/2, defined on the largest interval containing x=1 on which it is a solution.JEE Advanced 2017 Paper 1 · hard

JEE Advanced 2016

Let y(x) be the solution of (1+x^2dy/dx+2xy=2x with y(0)=0.JEE Advanced 2016 Paper 1 · medium
The curve y=y(x), x>1, satisfies the differential equation 2xy dy/dx=x^2+y^2 and passes through (4, 2√3).JEE Advanced 2016 Paper 2 · hard

Other Mathematics topics

Area Under Curves 13 Binomial Theorem 10 Complex Numbers 24 Conic Sections 34 Differentiation and Application of Derivatives 20 Indefinite and Definite Integrals 18 Limits 19 Matrices and Determinants 28 Permutations and Combinations 18 Probability 38 Quadratic Equations 12 Sequences and Series 11 Sets, Relations and Functions 8 Straight Lines and Circles 10 Three Dimensional Geometry 22 Trigonometry and Inverse Trigonometric Functions 18 Vector Algebra 9