Discussion
Consider the following statements about partial differential equations. 1. Eliminating an arbitrary function raises the order by one for each function 2. The general solution contains arbitrary functions rather than only constants 3. The type of a second-order equation follows from the sign of \( B^{2} - 4AC \)
Answer: B
All three hold. The presence of arbitrary functions is the essential difference from the ordinary case, and it is why one boundary curve rather than a few numbers is needed to pin a solution down. The discriminant test mirrors the classification of conics, and for the same algebraic reason
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