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Three of these are wrong. Find the one that holds.

Exercise and reference answers

Questions
  1. Question
    Three of these statements about degree are false.
    Choices
    1. Item
      Defined only for polynomial forms
      Correct
      Yes
    2. Explanation
      Order and degree are independent.
      Item
      Always equals the order
    3. Explanation
      Non-polynomial forms have no degree.
      Item
      Every equation has one
    4. Explanation
      A degree is a positive integer.
      Item
      It may be a fraction
  2. Question
    Three of these statements about solutions are false.
    Choices
    1. Item
      Its constants number the order
      Correct
      Yes
    2. Explanation
      It is free of them, which is what makes it particular.
      Item
      A particular solution keeps constants
    3. Explanation
      The count matches the order, which may exceed one.
      Item
      A general solution has one constant
    4. Explanation
      Satisfying the equation is the definition of a solution.
      Item
      A solution need not satisfy it

Explanation

Each trap drops the polynomial condition or miscounts the constants. Source: syllabus Maths Part II, Ch 9 Differential Equations.
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