Solve all Q44 explaining detailly each step 40. The table shows corresponding values of x and y obtained experimentally. It is given that xand y are connected by a relation of the form y = ax", where a and b are constants. Bydrawing a suitable linear graph, estimate the values of a and b to one decimal place.X1.72.33.24.35.9Y28.7115.0525.02100.08800.041. Solve the differential equationdy- xy – X = 0, given that y = 0 when x = 0.%3dx42. i) Sketch the curve y = 3x² – 12x and hence find the area of the region bounded by the curveand 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"%3D21) and the lines x = 0 and x = 6 about the x-axis. 'Find also the x-coordinate of the centroidof the solid generated.43. The table shows corresponding values of x and y obtained experimentally. By drawing asuitable graph relating log10x and log10y, show that these values support the hypothesis that xand y are connected by a relationship of the form: y =px", where p and q are constants. Useyour graph to estimate the values of p and q to one decimal place. Hence estimate the valueof , ydx dx. Use the trapezium rule to obtain anóther estimate for J, ydx9-2456.61280.03493.97963.3350.7dyY44. Solve the differential equation xy 1+y, given that x = 2, y = 045. The table shows corresponding values of x and y obtained experimentally.dx0.500.250.170.130.100.0830.070.380.250.190.150.130.110.09VIt is given that x and y are related by an equation of the formwhere a and b areconstants.By drawing a suitable linear graph relating - and- estimate the value of a and b correct toytwo decimal places.46. Two quantities x and y are known to be connected by a law of the form y = a (x+2)", where aand n are constants. Using the given table of values below, plot log y, against log(x+2) andhence find, to one decimal place the approximate values ofn and a.1Y1.060.580.380.270.2047. Find the area of the finite region bounded by the curve: y=xlnx, the x-axis and the lines x2.48. Solve the differential equation y(1+x*)-2(1+y*) = 0, given that y = 0 and x = 0.dydx49. The variable x and y tabulated below were obtained in an experiment and are thought to obeya law of the form:y = a(x – 1)n.5.6.139.162025Y6.57.07.157.561

We need to solve the differential equation xydydx=1+y2 , x=2 ,y=0 Consider: xydydx=1+y2 ⇒y1+y2dy=dxx…

Answered: dy 44. Solve the differential equation…

Math

Advanced Math

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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Solve all Q44 explaining detailly each step

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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