18. 9y" – 6y' + y = 0, y(0) = 3, y'(0) = 1 %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Transcribed Image Text:18-27
IVPS, SOME WITH DISCONTINUOUS
INPUT
Using the Laplace transform and showing the details, solve
18. 9y" - бу + у %3D0, у(0) %3D 3, у (0) %3D 1
19. y" + 6y' + 8y = e-3t – e-, y(0) = 0, y'(0) = 0
20. y" + 10y' + 24y = 14412, y(0) = 19/12,
y'(0) = -5
21. y" + 9y = 8 sin t if 0 <t < T and 0 if t > T;
y(0) = 0, y'(0) = 4
22. y" + 3y' + 2y = 4t if 0 <t< 1 and 8 if t> 1;
y(0) = 0, y'(0) = 0
23. y" + y' - 2y = 3 sin t - cos t if 0 <t < 2# and
3 sin 2t – cos 2t if t> 2T; y(0) = 1, y'(0) = 0
24. y" + 3y' + 2y = 1 if 0 <t<1 and 0 if t > 1;
y(0) = 0, y'(0) = 0
25. y" + y = t if 0 <t<1 and 0 if t> 1; y(0) = 0,
y' (0) = 0
26. Shifted data. y" + 2y' + 5y = 10 sin t if 0 <t< 2T
and 0 if t> 27; y(T) = 1, y'(T) = 2e¯™
27. Shifted data. y" + 4y = 812 if 0<t< 5 and 0 if
t> 5; y(1) = 1 + cos 2, y'(1) = 4 - 2 sin 2
-5t
%3D
%3D
%3D
%3D
%3D
%3D
2
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