The equation $xy\frac{{{\delta ^2}z}}{{\delta {x^2}}} - \left( {{x^2} - {y^2}} \right)\frac{{{\delta ^2}z}}{{\delta x\delta y}} - xy\frac{{{\delta ^2}z}}{{\delta {y^2}}} + y\frac{{\delta z}}{{\delta x}} - \frac{{\delta z}}{{\delta y}} = 2\left( {{x^2} - {y^2}} \right)$ is classified as:

Question

The equation $xy\frac{{{\delta ^2}z}}{{\delta {x^2}}} - \left( {{x^2} - {y^2}} \right)\frac{{{\delta ^2}z}}{{\delta x\delta y}} - xy\frac{{{\delta ^2}z}}{{\delta {y^2}}} + y\frac{{\delta z}}{{\delta x}} - \frac{{\delta z}}{{\delta y}} = 2\left( {{x^2} - {y^2}} \right)$ is classified as:

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parabolic

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elliptic

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hyperbolic for all x, y (≠ 0)

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hyperbolic for x = 0, y = 0; elsewhere parabolic

1.	The equation \(xy\frac{{{\delta ^2}z}}{{\delta {x^2}}} - \left( {{x^2} - {y^2}} \right)\frac{{{\delta ^2}z}}{{\delta x\delta y}} - xy\frac{{{\delta ^2}z}}{{\delta {y^2}}} + y\frac{{\delta z}}{{\delta x}} - \frac{{\delta z}}{{\delta y}} = 2\left( {{x^2} - {y^2}} \right)\) is classified as:
A.	elliptic
B.	hyperbolic for all x, y (≠ 0)
C.	parabolic
D.	hyperbolic for x = 0, y = 0; elsewhere parabolic
Answer» C. parabolic

The equation \(xy\frac{{{\delta ^2}z}}{{\delta {x^2}}} - \left( {{x^2} - {y^2}} \right)\frac{{{\delta ^2}z}}{{\delta x\delta y}} - xy\frac{{{\delta ^2}z}}{{\delta {y^2}}} + y\frac{{\delta z}}{{\delta x}} - \frac{{\delta z}}{{\delta y}} = 2\left( {{x^2} - {y^2}} \right)\) is classified as:

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