Start learning →

MP Board Class 12 (MPBSE) Differential Equations — practice questions

Explore 32 free Differential Equations questions in MP Board Class 12 (MPBSE) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Differential Equations with Quill →

Differential Equations questions and exercises with answers

Showing questions 1–30 of 32.

The ORDER and DEGREE of the DE (d²y/dx²)³ + (dy/dx)⁵ + y = 0 are:Read the answer and worked solution →The general solution of a 3rd-order DE contains how many arbitrary constants?Read the answer and worked solution →The DE dy/dx = y/x is best solved by:Read the answer and worked solution →For the linear DE dy/dx + (1/x)y = x, the INTEGRATING FACTOR μ(x) is:Read the answer and worked solution →If a population grows exponentially as dN/dt = 0.1 N (with t in years), the DOUBLING TIME is:Read the answer and worked solution →By Newton's law of cooling, a hot tea cup at 90°C in a room at 25°C cools so that:Read the answer and worked solution →A mass on a spring obeys d²x/dt² + ω²x = 0 (SHM). The period of oscillation is:Read the answer and worked solution →Complete the definition of order and degreeRead the answer and worked solution →True or false: order and degreeRead the answer and worked solution →General solution or particular solution?Read the answer and worked solution →Match each method to the form it solvesRead the answer and worked solution →Recognising the typeRead the answer and worked solution →Complete the definition of a differential equationRead the answer and worked solution →Order the steps: solve by separating variablesRead the answer and worked solution →Tap every statement true of a general solutionRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →True or false: methods of solutionRead the answer and worked solution →Order, degree, or neither?Read the answer and worked solution →Counting arbitrary constantsRead the answer and worked solution →Match each term to its meaningRead the answer and worked solution →Flip and pair: form with nameRead the answer and worked solution →Order the reasoning: from equation to particular solutionRead the answer and worked solution →True or false: the Historical NoteRead the answer and worked solution →Tap every equation type the chapter coversRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: forms and methodsRead the answer and worked solution →Reading definitions backRead the answer and worked solution →

Worked practice questions

The ORDER and DEGREE of the DE (d²y/dx²)³ + (dy/dx)⁵ + y = 0 are:

  1. Order 3, degree 2
  2. Order 2, degree 3
  3. Order 5, degree 1
  4. Order 2, degree 5
Show answer and solution

Correct answer: B. Order 2, degree 3

Order = highest derivative present = d²y/dx² → 2. Degree = power of highest-order derivative = (d²y/dx²)³ → 3.

Open this question →

The general solution of a 3rd-order DE contains how many arbitrary constants?

  1. One arbitrary constant
  2. Two arbitrary constants
  3. Three arbitrary constants
  4. Six arbitrary constants
Show answer and solution

Correct answer: C. Three arbitrary constants

Number of arbitrary constants in general solution = order of the DE. For 3rd-order, 3 constants. Particular solution fixes them via 3 initial conditions.

Open this question →

The DE dy/dx = y/x is best solved by:

  1. Variable separable (the easiest first try)
  2. Bernoulli's substitution v = y^(1−n)
  3. Integrating factor as linear DE
  4. Auxiliary equation as second-order
Show answer and solution

Correct answer: A. Variable separable (the easiest first try)

We have dy/dx = y/x → dy/y. That is dy/dx = dx/x → ln|y|. That is dy/dx = ln|x| + C → y. So dy/dx = Ax. **Variable separable:** separate variables, integrate both sides.

Open this question →

How to practise

  1. Choose a Differential Equations question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

Vectors & 3D GeometryBinomial TheoremGeometryPermutations and CombinationsProbability & StatisticsSequencesSequences and SeriesThree Dimensional Geometry