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Match the first-order equation with the method it calls for. 1. \( Pp + Qq = R \)   2. \( z = px + qy + f(p,q) \)   3. Neither of the standard forms   P. Replace \( p \) and \( q \) by constants   Q. Subsidiary equations \( dx/P = dy/Q = dz/R \)   R. Charpit's auxiliary equation

  • A.1-Q, 2-R, 3-P
  • B.1-P, 2-Q, 3-R
  • C.1-R, 2-P, 3-Q
  • D.1-Q, 2-P, 3-R

Answer: D

Lagrange's linear form is integrated through its subsidiary equations. Clairaut's form needs nothing more than replacing the two derivatives by constants. Anything outside the standard types goes to Charpit's method, which is general but longer

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