Start learning →

AMUEEE Differential Equations — practice questions — page 3

Explore 73 free Differential Equations questions in AMUEEE 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 61–73 of 73.

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 →Which belongs to which idea?Read the answer and worked solution →True or false: what a solution isRead the answer and worked solution →

Worked practice questions

True or false: methods of solution

Read exercise and reference answers
Questions
  1. Statement is true
    Yes
    Statement
    Variable separable needs the x and y terms to split completely.
  2. Statement is true
    Yes
    Statement
    A first order linear equation has the form dy/dx + Py = Q.
  3. Statement is true
    No
    Statement
    In that form, P and Q may be functions of y.
  4. Statement is true
    Yes
    Statement
    A homogeneous differential equation involves functions homogeneous of degree zero.
  5. Statement is true
    No
    Statement
    Every equation is separable.
Which method applies, and when. Source: syllabus Maths Part II, Ch 9 Differential Equations.

Open this exercise →

Order, degree, or neither?

Read exercise and reference answers
Items
  1. Item
    Order of the highest derivative present
    Category
    Order
  2. Item
    Tells you how many arbitrary constants to expect
    Category
    Order
  3. Item
    Highest power of the highest order derivative
    Category
    Degree
  4. Item
    Needs the equation to be polynomial in derivatives
    Category
    Degree
  5. Item
    The function that satisfies the equation
    Category
    Neither
Categories
  1. Item
    Order
  2. Item
    Degree
  3. Item
    Neither
Sorting the descriptions by which property they name. Source: syllabus Maths Part II, Ch 9 Differential Equations.

Open this exercise →

Counting arbitrary constants

Read exercise and reference answers
Questions
  1. Question
    A first order equation's general solution carries
    Choices
    1. two
    2. none
    3. one arbitrary constant
    Correct choice
    one arbitrary constant
  2. Question
    A second order equation's general solution carries
    Choices
    1. two arbitrary constants
    2. one
    3. none
    Correct choice
    two arbitrary constants
  3. Question
    A particular solution carries
    Choices
    1. one
    2. no arbitrary constants
    3. as many as the order
    Correct choice
    no arbitrary constants
The order fixes how many constants a general solution carries. Source: syllabus Maths Part II, Ch 9 Differential Equations.

Open this exercise →

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

SequencesProbability & StatisticsBinomial TheoremSequences and SeriesGeometryLinear ProgrammingLimits and ContinuityPermutations and Combinations