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Differential Equations Questions

Practice 42 Differential Equations questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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42
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0
Easy
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40
Medium
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2
Hard
Practice by Exam:Mathematics(41)Physics(1)

About Differential Equations — practice questions, PYQs & concepts

Differential Equations is a frequently-tested topic on Mathematics, Physics. ExamTest.live currently lists 42 Differential Equations questions spanning previous-year papers from 2004 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Differential Equations weight in competitive exams

Across our Differential Equations question bank, the largest sources are Mathematics (41) and Physics (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 0 easy Differential Equations questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Differential Equations Questions(1–42 of 42)

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Q1mediummcqMathematicsMathematics Mock Test - 62026
9% accuracy
What is the solution of the differential equation ?
Q2mediummcqMathematicsMathematics Mock Test - 62026
13% accuracy
The order and degree of the differential equation are respectively:
Q3mediummcqMathematicsMathematics Mock Test - 62026
13% accuracy
The differential form of the equation is:
Q4mediummcqMathematicsMathematics Mock Test - 62026
9% accuracy
The solution of the differential equation is:
Q5mediummcqMathematicsMathematics Mock Test - 102026
9% accuracy
The solution of the differential equation is:
Q6mediummcqMathematicsMathematics Mock Test - 12026
0% accuracy
The differential equation representing the family of curves is:
Q7mediummcqMathematicsMathematics Mock Test - 12026
9% accuracy
The order and degree of the differential equation are respectively:
Q8mediummcqMathematicsMathematics Mock Test - 102026
18% accuracy
The solution of is:
Q9mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
The order and degree of the differential equation:
Q10mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
The curve satisfying the differential equation and passing through the point is:
Q11mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
If at a point on the curve the slope of the line tangent to the curve is equal to , then the function is:
Q12mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
The integrating factor of the differential equation is given by:
Q13mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
What is the degree of the differential equation ?
Q14mediummcqMathematicsMathematics Mock Test - 42026
100% accuracy
Solve the differential equation .
Q15mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
For the given ordinary differential equation, , the integrating factor will be equal to:
Q16mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
Rate of growth of bacteria is proportional to the number of bacteria present at time. If is the number of bacteria present at any instant , then which one of the following is correct? (Let the proportional constant equal to )
Q17mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
What is the general solution of ? (where is a constant of integration)
Q18mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
What is the degree of the following differential equation?
Q19mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
The order and degree of the differential equation are:
Q20mediummcqMathematicsAIEEE 20062026
0% accuracy
The differential equation whose solution is , where and are arbitrary constants, is of:
Q21mediummcqMathematicsAIEEE 20072026
0% accuracy
The differential equation of all circles passing through the origin and having their centres on the -axis is:
Q22mediummcqMathematicsMathematics Mock Test - 112026
The solution of the differential equation is:
Q23mediummcqMathematicsMathematics Mock Test - 82026
The differential form of the equation is:
Q24mediummcqMathematicsMathematics Mock Test - 82026
The solution of is:
Q25mediummcqMathematicsMathematics Mock Test - 32026
The function is a solution to the differential equation:
Q26mediummcqMathematicsAIEEE2026
The differential equation representing the family of curves , where is a parameter, is of order and degree respectively:
Q27mediummcqMathematicsAIEEE2026
If , then the solution of the equation is:
Q28mediummcqMathematicsAIEEE-CBSE-ENG-032026
The degree and order of the differential equation of the family of all parabolas whose axis is the -axis, are respectively:
Q29mediummcqMathematicsAIEEE-CBSE-ENG-032026
The solution of the differential equation , is:
Q30mediummcqMathematicsAIEEE2026
The solution of the differential equation satisfying the condition is:
Q31mediummcqMathematicsAIEEE2026
The differential equation of the family of circles with fixed radius units and centre on the line is:
Q32mediummcqMathematicsAIEEE 20092026
The differential equation which represents the family of curves , where and are arbitrary constants is:
Q33mediummcqMathematicsAIEEE2026
Solution of the differential equation , is:
Q34mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
If and , then is equal to:
Q35mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
Let be the purchase value of an equipment and be the value after it has been used for years. The value depreciates at a rate given by differential equation , where is a constant and is the total life in years of the equipment. Then the scrap value of the equipment is:
Q36mediummcqMathematicsAIEEE 20122026
The population at time of a certain mouse species satisfies the differential equation . If , then the time at which the population becomes zero is:
Q37mediummcqMathematicsJEE Main2026
At present, a firm is manufacturing items. It is estimated that the rate of change of production w.r.t. additional number of workers is given by . If the firm employs more workers, then the new level of production of items is:
Q38mediummcqMathematicsMathematics Mock Test - 32026
The degree of the given equation is
Q39mediummcqMathematicsMathematics Mock Test - 32026
Solve
Q40hardmcqMathematicsAIEEE 20042004
0% accuracy
The solution of the differential equation is
Q41hardmcqMathematicsAIEEE 20042004
0% accuracy
The differential equation for the family of curves where is an arbitrary constant is
Q42mediummcqPhysicsPhysics
6% accuracy
Consider a water tank as shown in the figure. It has one wall at and is very wide in the direction. When filled with a liquid of surface tension and density , the liquid surface makes an angle () with the -axis at . If is the height of the surface, then the equation for is:(Take and as acceleration due to gravity)

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Frequently Asked Questions

How many Differential Equations questions are on ExamTest.live?▼
We have 42 Differential Equations questions spread across 1 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
Are Differential Equations MCQs free?▼
Yes. All Differential Equations questions, answers, and explanations on ExamTest.live are completely free. No account or subscription required.
Which exams include Differential Equations questions?▼
Differential Equations questions are commonly asked in Mathematics, Physics. You can filter by exam using the links above.
How do I practice Differential Equations questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.