Differential Equations JEE Mains Questions - List Of Most Asked Questions With Solutions

NTA will shortly release the JEE Main Syllabus 2025 at jeemain.nta.ac.in. Last Year, the complete syllabus of JEE Main underwent some major changes. According to the latest syllabus guidelines, the weightage of Maths has dropped to 22.5%. Due to these changes in the syllabus, certain shifts in chapter-wise weightage have been observed. Differential Equations are among such topics. It’s among the least weightage topics in JEE Main Maths Syllabus 2025. This chapter holds 1.39% weightage in the whole syllabus.

• Differential Equation is a part of the General Maths section, and every year around 2-3 questions are asked from this chapter. Due to the drop in weightage, you can expect 1-2 questions in JEE Main 2025.
• Differential Equation in JEE Mains Maths Syllabus 2025 covers all the basic concepts on units and measurements, fundamentals of units, dimensions etc.

Aspirants consider Differential Equation as one of the Easiest Chapters in Maths for JEE Main 2025. Even though this chapter has the least weightage in the syllabus, to develop a strong foundation in physics, this particular chapter plays a pivotal role. Hence the candidates need to develop a clear understanding of this chapter. The list of most asked questions from this chapter will help the students with their preparation.

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Some of the most important topics for differential equations in JEE Main include:

• Variable separable equations
• Homogeneous differential equations
• Linear differential equations
• Exact differential equations
• Integrating factor method
• Second-order differential equations
• Reduction of order
• Variation of parameters
• Applications in physics and engineering
• Systems of differential equations

Differential Equations JEE Mains Questions -

List Of Most Asked Questions With Solutions

In the (JEE) Main, the topic of Physics and Measurement often features questions that have appeared multiple times in previous years. Many questions in this section are either repeated or follow similar patterns, with only minor changes, such as different numerical values or slight modifications in wording.Certain questions have been repeated as many as five times.

Here are some of the most frequently asked and repeated questions:

Question 1:

If y = e^x is a solution of the differential equation then the values of a and b are:

(This question has been asked thrice-JEE Main 2021,JEE Main 2018,JEE Main 2017 )

Options:

A) a = 1, b = 1

B) a = 2, b = 1

C) a = 1, b = 2

D) a = 2, b = 2

Solution:

Substituting y = e^x into the given differential equation results in 1+a+b=0

Solving this gives a = 2 and b = 1.

Correct answer: B

Year: 2021

Question 2:

The solution of the differential equation

(This question has been asked thrice-JEE Main 2021,JEE Main 2018,JEE Main 2020 )

Options:

A) y=ccos⁡(x)

B) y=csin⁡(x)

C) y=cesin⁡(x)

D) y=cecos⁡(x)

Solution:

Using the method of separation of variables, integrating both sides, we get

Correct answer: C

Year: 2020

Question 3:

The integrating factor of the differential equation

(This question has been asked thrice-JEE Main 2021,JEE Main 2018,JEE Main 2019 )

Options:

A) x

B) 1x^{-1}

C) x^2

D) ex

Solution:

This is a linear differential equation, and the integrating factor is

Correct answer: B

Year: 2019

Question 4:

The general solution of the differential equation

(This question has been asked thrice-JEE Main 2021,JEE Main 2018 )

Solution:

This is a first-order linear equation, and solving using the integrating factor method gives y=ce−x+x+1.

Correct answer: C

Year: 2018

Question 5:

The particular solution of the differential equation

(This question has been asked thrice-JEE Main 2017,JEE Main 2022,JEE Main 2024 )

Options:

A) y=x3+1

B) y=x3+2

C) y=x3+3

D) y=x3+4

Solution:

Integrating the equation Using the condition y(1)=2y, we get c=1. So, the solution is y = x^3 + 1.

Correct answer: A

Year: 2017