💬 Discord
Login

Differential Equations Practice Questions

JEE · Mathematics · 2044 free MCQs with instant results and detailed explanations.

2044
Total
480
Easy
831
Medium
733
Hard

Start Practicing Differential Equations

Take a timed quiz or customize your practice session

Quick Quiz (10 Qs) → Mock Test (25 Qs) ⚙ Customize

Topics in Differential Equations

Order and Degree 361
Linear DE 221
Homogeneous DE 334
Bernoulli's Equation 201
Variable Separable 269
Homogeneous Equations 245
Exact Equations 235
Applications 178

Sample Questions from Differential Equations

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the degree of the equation (dy/dx)^3 + y = x?
A. 3
B. 1
C. 0
D. Undefined
Show Answer & Explanation
Correct Answer: A
The degree of a differential equation is the power of the highest derivative when the equation is polynomial in derivatives. Here, (dy/dx) is raised to the power of 3.
Q2
Easy
For the differential equation d²y/dx² + 4dy/dx + 4y = 0, what is the order and degree?
A. Order 2, Degree 1
B. Order 1, Degree 2
C. Order 2, Degree 2
D. Order 1, Degree 1
Show Answer & Explanation
Correct Answer: A
This equation contains the second derivative d²y/dx², indicating the order is 2. It is linear in form, so the degree is 1.
Q3
Easy
What is the order of the differential equation dy/dx + 3y = sin(x)?
A. 1
B. 2
C. 0
D. 3
Show Answer & Explanation
Correct Answer: A
The order of a differential equation is determined by the highest derivative present. Here, only the first derivative dy/dx is present, making the order 1.
Q4
Medium
What is the order of the differential equation y'' + 3y' - 2y = 0?
A. 2
B. 1
C. 3
D. 0
Show Answer & Explanation
Correct Answer: A
The order of a differential equation is the highest derivative present. Here, y'' is the highest derivative, which is second.
Q5
Medium
Determine the degree of the equation (dy/dx)^2 + y = x.
A. 1
B. 2
C. 0
D. not defined
Show Answer & Explanation
Correct Answer: B
The degree of a differential equation is the power of the highest derivative after it has been made polynomial. Here, (dy/dx)^2 is the highest derivative raised to the power of 2.
Q6
Medium
What is the order of the differential equation (d^3y/dx^3) + 5(dy/dx) = sin(x)?
A. 1
B. 2
C. 3
D. 0
Show Answer & Explanation
Correct Answer: C
The order is determined by the highest derivative. Here, d^3y/dx^3 indicates the third derivative, hence the order is 3.
Q7
Medium
If the differential equation is of the form (dy/dx) + P(x)y = Q(x), what is the order of this equation?
A. 1
B. 2
C. 3
D. 0
Show Answer & Explanation
Correct Answer: A
This form represents a first-order linear differential equation, hence its order is 1.
Q8
Hard
What is the order of the differential equation: dy/dx + (x^2)y = x?
A. 1
B. 2
C. 0
D. 3
Show Answer & Explanation
Correct Answer: A
The order of a differential equation is the highest derivative present. Here, the highest derivative is dy/dx, which is of order 1.
Q9
Hard
Determine the degree of the differential equation: (dy/dx)^2 + y^2 = x.
A. 1
B. 2
C. 3
D. 0
Show Answer & Explanation
Correct Answer: B
The degree of a differential equation is the power of the highest order derivative after clearing any fractions or radicals. Here, (dy/dx)^2 is raised to power 2.
Q10
Hard
Identify the order and degree of the equation: (d^2y/dx^2) + e^y = 0.
A. Order: 2, Degree: 1
B. Order: 1, Degree: 2
C. Order: 2, Degree: 2
D. Order: 2, Degree: 0
Show Answer & Explanation
Correct Answer: A
The order is 2 due to the second derivative present, and the degree is 1 since it’s not raised to any power beyond 1.

Showing 10 of 2044 questions. Start a quiz to practice all questions with scoring and timer.

Practice All 2044 Questions →

More Mathematics Chapters

1 Sets Relations and Functions
1652 Qs →
2 Complex Numbers
1613 Qs →
3 Matrices and Determinants
1781 Qs →
4 Permutations and Combinations
1645 Qs →
5 Limits Continuity and Differentiability
1661 Qs →
6 Integral Calculus
1623 Qs →
7 Coordinate Geometry
1290 Qs →
8 Vector Algebra and 3D Geometry
1678 Qs →

Other JEE Subjects

⚡ Physics → ⚗️ Chemistry →

Differential Equations — JEE Mathematics Practice Questions Online

This page contains 2044 practice MCQs for the chapter Differential Equations in JEE Mathematics. The questions are organized by difficulty — 480 easy, 831 medium, 733 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 8 topics, giving you comprehensive coverage of the entire chapter.