Constructing A Solution to a PDEConstruct a general solution involving two arbitrary functions to the PDE6²u(x,t) _ ô²u(x,1)a²u(x,t)20-Ôx²ôtôxover the range -00 < x < +o∞ and 0 < t.Determine the specific solution given the initial conditionsди(х, )и(х,0) — х?and2xfor- 00 < x < +00.

Comparing it with Auxx+Butx+Cutt form, we get A=20, B=-1, C=-1. Then, B2-4AC=(-1)2-4(20)(-1)=1+80=81…

Construct a general solution involving two arbitrary functions to the PDE 20 0Pu(x, 1) _ ô²u(x, 1) _ ô²u(x,t) Ôx² ôtôx over the range -∞ < x < +0 and 0 < t. Determine the specific solution given the initial conditions ди(х, ) | u(x,0) = x² and 2x for - 0 < x < +00. -0

Construct a general solution involving two arbitrary functions to the PDE 20 0Pu(x, 1) _ ô²u(x, 1) _ ô²u(x,t) Ôx² ôtôx over the range -∞ < x < +0 and 0 < t. Determine the specific solution given the initial conditions ди(х, ) | u(x,0) = x² and 2x for - 0 < x < +00. -0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Constructing A Solution to a PDE
Construct a general solution involving two arbitrary functions to the PDE
6²u(x,t) _ ô²u(x,1)
a²u(x,t)
20-
Ôx²
ôtôx
over the range -00 < x < +o∞ and 0 < t.
Determine the specific solution given the initial conditions
ди(х, )
и(х,0) — х?
and
2x
for
- 00 < x < +00.

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