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Discussion

Charpit's method is used for a first-order partial differential equation when

  • A.the boundary conditions are given on a characteristic curve
  • B.the equation falls into none of the standard solvable types
  • C.the equation is linear in the two first derivatives
  • D.the equation is of the second order

Answer: B

Charpit's method is the general procedure: it adjoins an auxiliary equation in \( dp \), \( dq \), \( dx \), \( dy \) and \( dz \), from which a second relation between \( p \) and \( q \) is found and integrated. The standard types are shortcuts worth using where they apply, and a linear equation is Lagrange's case

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