Consider the inhomogeneous partial differential equation in T(x, t) given by ə 1 OT Ox Ox(3+2x²) Choose v(x) such a way that the substitution T(x, t) = v(x) + 6(x, t) gives rise to a homogeneous partial differential equation in p(x, t). 0 ỐT CT = 4 + + ôt ôt² v(x) = 4x² + 4xª O It is not possible to find v(x). v(x) = 4x²8x¹ B v(x)=8x² + 4x v(x) 6x²+2x+

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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Consider the inhomogeneous partial differential equation
in T(x, t) given by
ə
1 OT
Ox(3+2x²) Ox
Choose v(x) such a way that the substitution
T(x, t) = v(x) + 6(x, t)
gives rise to a homogeneous partial differential equation
in p(x, t).
0
=
B
CT
ỐT
4 + +
ôt ôt²
v(x) = 4x² + 4xª
O It is not possible to find v(x).
v(x) = 4a²8aª
v(x)=8x² + 4x
v(x) 6x²+2x+
Transcribed Image Text:Consider the inhomogeneous partial differential equation in T(x, t) given by ə 1 OT Ox(3+2x²) Ox Choose v(x) such a way that the substitution T(x, t) = v(x) + 6(x, t) gives rise to a homogeneous partial differential equation in p(x, t). 0 = B CT ỐT 4 + + ôt ôt² v(x) = 4x² + 4xª O It is not possible to find v(x). v(x) = 4a²8aª v(x)=8x² + 4x v(x) 6x²+2x+
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