Use Green's theorem to evaluate S, (5xy + x² + y²) dx + (x² – y)dy whereC is a closed curve that is formed by y = x, x? + y? = 4 and y-axis for whichх, у > 0.(a)Given two points A(3, 0) and B(÷), find the work done by the followingforce field in moving a particle along x2 + y2 = 9 from the point A to B:F = (x + y)ï+ x²j(b)33%3D Given a partial differential equation Uxx+ Utt = 0 for 0

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Use Green's theorem to evaluate S, (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is formed by y = x, x? + y² = 4 and y-axis for which (a) х, у > 0. Given twvo points 4(3 0) ond Pl 3 3 )

Use Green's theorem to evaluate S, (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is formed by y = x, x? + y² = 4 and y-axis for which (a) х, у > 0. Given twvo points 4(3 0) ond Pl 3 3 )

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

Use Green's theorem to evaluate S, (5xy + x² + y²) dx + (x² – y)dy where
C is a closed curve that is formed by y = x, x? + y? = 4 and y-axis for which
х, у > 0.
(a)
Given two points A(3, 0) and B(÷), find the work done by the following
force field in moving a particle along x2 + y2 = 9 from the point A to B:
F = (x + y)ï+ x²j
(b)
3
3
%3D

Given a partial differential equation Uxx+ Utt = 0 for 0 <x < 1,0<t<1.
%3D
Solve the given equation with the following conditions
U(0, t) = 0,0 <t<1
U (x, 0) = 0,0 <x < 1
U (x, 1) = 0,0 <x< 1.
(a)
Hence, based on your answer from part (a), find the solution of U(x, t) given
the condition U(1, t) = t + 1,0 <t < 1.
(b)

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ISBN:

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