Question

For the partial differential equation −5 ∂x 2 ∂ 2 u −4 ∂x∂y ∂ 2 u +1 ∂y 2∂ 2 u−3 ∂x/∂u −8 ∂y/∂u

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−5u=0 the discriminant is The PDE is (check all that apply)
A. hyperbolic
B. parabolic
C. elliptic
D. separable
E. inseparable

Answer 1

The discriminant of the given partial differential equation is positive, indicating that the equation is hyperbolic.

Step-by-step explanation:

The discriminant of a partial differential equation can be used to determine its classification. The discriminant is given by the expression b^2 - 4ac, where a, b, and c are coefficients of the partial differential equation.

In this particular equation, the discriminant can be calculated as (-4)^2 - 4*(-5)*1 = 16 + 20 = 36.

Since the discriminant is positive, the equation is classified as hyperbolic. Therefore, option A is correct.