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AP Intermediate 2nd Year Differential Equations — practice questions — page 2

Explore 88 free Differential Equations questions in AP Intermediate 2nd Year 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 31–60 of 88.

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 →Which belongs to which idea?Read the answer and worked solution →True or false: what a solution isRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Assertion and reason: forms and methodsRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every equation type the chapter coversRead the answer and worked solution →

Worked practice questions

A mass on a spring obeys d²x/dt² + ω²x = 0 (SHM). The period of oscillation is:

  1. $2\pi \omega$ (inverse)
  2. $T = 2\pi/\omega$ (the period formula)
  3. $T = 1/\omega$ (frequency reciprocal)
  4. $T = \omega^2$ (squared)
Show answer and solution

Correct answer: B. $T = 2\pi/\omega$ (the period formula)

**SHM:** x(t) = A cos(ωt + φ). Period T = 2π/ω. Frequency f = ω/(2π) = 1/T.

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Complete the definition of order and degree

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Missing parts
  1. Answer
    highest order
    Choices
    1. highest order
    2. lowest order
    3. first
  2. Answer
    polynomial
    Choices
    1. polynomial
    2. linear
    3. homogeneous
  3. Answer
    power
    Choices
    1. power
    2. coefficient
    3. root
Complete the statement
The order of a differential equation is the order of its {0} derivative. Its degree is defined only when the equation is a {1} equation in its derivatives, and it is then the highest {2} of the highest order derivative.
The two are defined differently, and only one of them always exists. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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True or false: order and degree

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Questions
  1. Statement is true
    Yes
    Statement
    The order is the order of the highest order derivative present.
  2. Statement is true
    No
    Statement
    Every differential equation has a degree.
  3. Statement is true
    Yes
    Statement
    Degree is defined only when the equation is polynomial in its derivatives.
  4. Statement is true
    Yes
    Statement
    A degree, when defined, is a positive integer.
  5. Statement is true
    No
    Statement
    Order and degree always have the same value.
The caveat on degree is the point of this round. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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