dy 44. Solve the differential equation xy- 1 + y, given that x = 2, y = 0 dx
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
Solve all Q44 explaining detailly each step
Transcribed Image Text:40. The table shows corresponding values of x and y obtained experimentally. It is given that x
and y are connected by a relation of the form y = ax", where a and b are constants. By
drawing a suitable linear graph, estimate the values of a and b to one decimal place.
X
1.7
2.3
3.2
4.3
5.9
Y
28.7
115.0
525.0
2100.0
8800.0
41. Solve the differential equation
dy
- xy – X = 0, given that y = 0 when x = 0.
%3
dx
42. i) Sketch the curve y = 3x² – 12x and hence find the area of the region bounded by the curve
and the lines y = 0, x = 0 and x =5.
ii) Find the volume generated by rotating completely the area bounded by the curve x = 3(y"
%3D
2
1) and the lines x = 0 and x = 6 about the x-axis. 'Find also the x-coordinate of the centroid
of the solid generated.
43. The table shows corresponding values of x and y obtained experimentally. By drawing a
suitable graph relating log10x and log10y, show that these values support the hypothesis that x
and y are connected by a relationship of the form: y =px", where p and q are constants. Use
your graph to estimate the values of p and q to one decimal place. Hence estimate the value
of , ydx dx. Use the trapezium rule to obtain anóther estimate for J, ydx
9-
2
4
56.6
1280.0
3493.9
7963.3
350.7
dy
Y
44. Solve the differential equation xy 1+y, given that x = 2, y = 0
45. The table shows corresponding values of x and y obtained experimentally.
dx
0.50
0.25
0.17
0.13
0.10
0.083
0.07
0.38
0.25
0.19
0.15
0.13
0.11
0.09
V
It is given that x and y are related by an equation of the form
where a and b are
constants.
By drawing a suitable linear graph relating - and- estimate the value of a and b correct to
y
two decimal places.
46. Two quantities x and y are known to be connected by a law of the form y = a (x+2)", where a
and n are constants. Using the given table of values below, plot log y, against log(x+2) and
hence find, to one decimal place the approximate values ofn and a.
1
Y
1.06
0.58
0.38
0.27
0.20
47. Find the area of the finite region bounded by the curve: y=xlnx, the x-axis and the lines x
2.
48. Solve the differential equation y(1+x*)-2(1+y*) = 0, given that y = 0 and x = 0.
dy
dx
49. The variable x and y tabulated below were obtained in an experiment and are thought to obey
a law of the form:y = a(x – 1)n.
5.
6.13
9.
16
20
25
Y
6.5
7.0
7.15
7.5
61
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