Question 1 Given (4x²y² + 2x³ +y³) dx + (3y²x + x³y + 4y) dy = 0. (a) Determine whether the given differential equation is exact. (b) If it is exact, then solve it.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question 1
Given (4x²y² + 2x³ +y³) dx + (3y²x + x³y + 4y) dy = 0.
(a) Determine whether the given differential equation is exact.
(b)
Question 2
If it is exact, then solve it.
By using table of Laplace transform, determine
(a)
(b)
the Laplace transform of the following functions:
i.
f(t) = sinh (V8t)
ii.
g(t) = 20 + te-8t
the inverse Laplace transform of the functions:
10
i.
G(S) == /2-25+3
ii.
F(s) =
S+5
(s-4)²+3*
Transcribed Image Text:Question 1 Given (4x²y² + 2x³ +y³) dx + (3y²x + x³y + 4y) dy = 0. (a) Determine whether the given differential equation is exact. (b) Question 2 If it is exact, then solve it. By using table of Laplace transform, determine (a) (b) the Laplace transform of the following functions: i. f(t) = sinh (V8t) ii. g(t) = 20 + te-8t the inverse Laplace transform of the functions: 10 i. G(S) == /2-25+3 ii. F(s) = S+5 (s-4)²+3*
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