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The general solution of \( p + q = 0 \) is

  • A.\( z = f(x) + f(y) \)
  • B.\( z = f(x - y) \)
  • C.\( z = f(x + y) \)
  • D.\( z = f(xy) \)

Answer: B

The subsidiary equations are \( dx/1 = dy/1 = dz/0 \). The last gives \( z = b \), and the first pair gives \( x - y = a \), so

\[ z \;=\; f(x - y). \]

Checking, \( p = f' \) and \( q = -f' \), which indeed sum to zero. The combination \( x + y \) would satisfy \( p - q = 0 \) instead

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