Class XII

To form a differential equation from a given function
  1. Differentiate the function once and add values to arbitrary constants
  2. Differentiate the function successively as many times as the number of arbitrary constants inthe given function and eliminate the arbitrary constants.
  3. Differentiate the function once and eliminate the arbitrary constants
  4. Differentiate the function twice and eliminate the arbitrary constants
General solution of a given differential equation
  1. contains exactly two arbitrary constants
  2. does not contain arbitrary constants
  3. contains exactly one arbitrary constant
  4. contains arbitrary constants depending on the order of the differential equation
Degree of a differential equation, when the equation is polynomial equation in y′ is
  1. Lowest power (positive integral index) of the lowest order derivative in the given differential equation.
  2. Lowest power (positive integral index) of the highest order derivative in the given differential equation
  3. Highest (positive integral index) of the lowest order derivative in the given differential equation.
  4. Highest power (positive integral index) of the highest order derivative in the given differential equation.
Order of a differential equation is defined as
  1. the order of the highest order derivative of the dependent variable
  2. the number of constant terms
  3. the number of derivative terms
  4. the order of the lowest order derivative ofthe dependent variable
Particular solution of a given differential equation
  1. can contain exactly two arbitrary constants
  2. can contain arbitrary constants
  3. can contain exactly one arbitrary constant
  4. does not contain arbitrary constants
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