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The singular solution of a first-order partial differential equation is obtained from the complete integral by

  • A.eliminating the constants between it and its derivatives with respect to them
  • B.setting all the arbitrary constants to zero
  • C.differentiating it once with respect to each independent variable
  • D.replacing each constant by an arbitrary function

Answer: A

The complete integral \( F(x,y,z,a,b) = 0 \) gives the singular solution when \( a \) and \( b \) are eliminated between it and \( \partial F/\partial a = 0 \), \( \partial F/\partial b = 0 \). Geometrically it is the envelope of the family. Setting the constants to zero merely picks one member, and replacing them by functions leads towards the general solution

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