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A particular solution of a partial differential equation is obtained by

  • A.taking the envelope of the family of surfaces
  • B.eliminating the arbitrary function from the general solution
  • C.adding the complete integral to the singular solution
  • D.assigning definite values to the constants of the complete integral

Answer: D

Fixing the constants selects one surface out of the two-parameter family, and that is what a particular solution is. The envelope of the family is the singular solution, a different object that need not belong to the family at all, and no meaning attaches to adding two solutions of a nonlinear equation

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