Du те Әи +(-u) =y-x. ду
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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Transcribed Image Text:3. Consider the PDE
By finding suitable functions A, 4 and such that
is an exact differential, and
du
Dr
(u-y) +(-u) =y-r.
du
where G is an arbitrary differentiable function.
Adr + µdy + vdz
A(u-y)+(x-u) + (y-2) = 0,
find two integrals for the PDE, and hence show that its general solution is given implicitly by
u(x, y) = -x-y+G(ry + (x+y)u(x, y))
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