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KCET Differential Equations — practice questions — page 2

Explore 52 free Differential Equations questions in KCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Differential Equations questions and exercises with answers

Showing questions 31–52 of 52.

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 →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

Match each method to the form it solves

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Matching pairs
  1. Left
    Variable separable
    Right
    all y terms go with dy, all x terms with dx
  2. Left
    Homogeneous method
    Right
    dy/dx = f(x, y) with f homogeneous of degree zero
  3. Left
    Linear method
    Right
    dy/dx + Py = Q with P, Q functions of x only
  4. Left
    A solution
    Right
    any function that satisfies the equation
Three methods, three recognisable forms. Choosing correctly is most of the chapter. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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Recognising the type

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Questions
  1. Question
    dy/dx + Py = Q with P, Q functions of x is called
    Choices
    1. homogeneous
    2. first order linear
    3. variable separable
    Correct choice
    first order linear
  2. Question
    An equation whose variables split completely is solved by
    Choices
    1. the linear method
    2. substitution y = vx
    3. variable separable
    Correct choice
    variable separable
  3. Question
    A homogeneous differential equation has f(x, y) homogeneous of degree
    Choices
    1. zero
    2. one
    3. two
    Correct choice
    zero
  4. Question
    A general solution contains arbitrary constants numbering
    Choices
    1. always one
    2. as many as the order
    3. none
    Correct choice
    as many as the order
Reading the form tells you the method before any integration starts. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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Complete the definition of a differential equation

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Missing parts
  1. Answer
    derivatives
    Choices
    1. derivatives
    2. integrals
    3. roots
  2. Answer
    independent
    Choices
    1. independent
    2. dependent
    3. arbitrary
  3. Answer
    solution
    Choices
    1. solution
    2. degree
    3. order
Complete the statement
A differential equation is an equation involving {0} of the dependent variable with respect to the {1} variable. A function that satisfies it is called its {2}.
The opening bullet of the summary. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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