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Exact Solutions > Systems of Partial Differential Equations > Linear Systems of Two Second-Order Partial Differential Equations

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1. Linear Systems of Two Second-Order Partial Differential Equations

  1. ut = auxx + b1u + c1w,   wt = awxx + b2u + c2w.
  2. ut = auxx + f1(t)u + g1(t)w,   wt = awxx + f2(t)u + g2(t)w.
  3. utt = kuxx + a1u + b1w,   wtt = kwxx + a2u + b2w.
  4. uxx + uyy = a1u + b1w,   wxx + wyy = a2u + b2w.

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