(c) Consider the following 2nd order PDE, Uxx + 2Uxy + 4U = 0. I (i) Write down its principal part and then determine the type (elliptic, parabolic or hyperbolic). (ii) Change the principal part of the above equation to a canonical form (i.e. without cross-derivatives).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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(c) Consider the following 2nd order PDE,
Uxx + 2Uxy + 4U, = 0.
I
(i) Write down its principal part and then determine the type (elliptic, parabolic
or hyperbolic).
(ii) Change the principal part of the above equation to a canonical form (i.e.
without cross-derivatives).
(d) Find all possible values of a, b, c so that U(x, t) = ax² + bt + ct² solves the heat
equation
UtUxx = 0, x > 0.
Transcribed Image Text:(c) Consider the following 2nd order PDE, Uxx + 2Uxy + 4U, = 0. I (i) Write down its principal part and then determine the type (elliptic, parabolic or hyperbolic). (ii) Change the principal part of the above equation to a canonical form (i.e. without cross-derivatives). (d) Find all possible values of a, b, c so that U(x, t) = ax² + bt + ct² solves the heat equation UtUxx = 0, x > 0.
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