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Match the equation with its type. 1. \( z_{xx} + z_{yy} = 0 \)   2. \( z_{t} = \alpha z_{xx} \)   3. \( z_{tt} = c^{2}z_{xx} \)   P. Parabolic   Q. Elliptic   R. Hyperbolic

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

Answer: A

The discriminant \( B^{2} - 4AC \) is \( -4 \), zero and \( 4c^{2} \) respectively. Negative gives elliptic, with data round a closed boundary; zero gives parabolic, marching forward from an initial state; positive gives hyperbolic, carrying disturbances along characteristics at finite speed

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