Solve Q72, 71 explaining detailly each step 62. The table below shows corresponding values of x and y which approximately satisfy arelation of the form. y = ax"X2346.75025077518753907200Where a and n are constants. By drawing a suitable linear graph, determine the values of aand n, correct to one decimal place.1+x63. Sketch the graph ofshowing clearly the asymptotes and the points where the curve meets1-xthe coordinates axes.64. The area bounded by the curve y = 3 + 2x – x and the line y= 3 is rotated completely aboutthe line y = 3. Find the volume of the solid of revolution obtained.%3D65. Expressin partial fractions. Hence, or otherwise, solve the differential equation(1+x)(1+3x)dy2(y+2)given that y = -1 when x = 0.dx(1+x)(1+3x)'66. The table below shows values of a continuous variable y corresponding to given values of x.346.X13.627.254.4108.8217.6Use the trapezium rule to find an estimate for , ydx(67. The expression y= ax²+ bx, is an approximation to a relation connecting two variables x andy, where a and b are constants. By using the values given in the table below, draw a suitablestraight line graph and use it to estimate the values of a and b.2346.112616217217514474dy= xy, given that y = 1, when x= 068. Solve the differential equation: (1 + x2)dx69. (In this question, you are advised to work throughout with 2 decimal places.)The table below shows corresponding values ofx and y obtained in a certain experiment.2.394.166.318.7012.011.596.9116.5931.7052.4887.103.63The relation connecting x and y is: y = x" where'2 and n are constants.By drawing a suitable linear graph relating log10 xand log10 y, calculate the values of 1 andn.dyX =-70. Obtain in the form: y = f(x), a particular solution of the differential equation:dx2xy, given that y = 0 when x = 0.71. Solve the differential equation x(1 – y) = -2y given that y = 2when x = e. Hence, show thatdxdyy = In (2)(-dy72. Solve the differential equation xdxy(2x² + 1)(.

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Answered: 71. Solve the differential equation…

Math

Advanced Math

71. Solve the differential equation x(1- y)2 = -2y given that y = 2when e Snow uiat dx y = In ()(-.

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 Q72, 71 explaining detailly each step

62. The table below shows corresponding values of x and y which approximately satisfy a
relation of the form. y = ax"
X
2
3
4
6.
7
50
250
775
1875
390
7200
Where a and n are constants. By drawing a suitable linear graph, determine the values of a
and n, correct to one decimal place.
1+x
63. Sketch the graph of
showing clearly the asymptotes and the points where the curve meets
1-x
the coordinates axes.
64. The area bounded by the curve y = 3 + 2x – x and the line y= 3 is rotated completely about
the line y = 3. Find the volume of the solid of revolution obtained.
%3D
65. Express
in partial fractions. Hence, or otherwise, solve the differential equation
(1+x)(1+3x)
dy
2(y+2)
given that y = -1 when x = 0.
dx
(1+x)(1+3x)'
66. The table below shows values of a continuous variable y corresponding to given values of x.
3
4
6.
X
13.6
27.2
54.4
108.8
217.6
Use the trapezium rule to find an estimate for , ydx(
67. The expression y= ax²+ bx, is an approximation to a relation connecting two variables x and
y, where a and b are constants. By using the values given in the table below, draw a suitable
straight line graph and use it to estimate the values of a and b.
2
3
4
6.
1
126
162
172
175
144
74
dy
= xy, given that y = 1, when x= 0
68. Solve the differential equation: (1 + x2)
dx
69. (In this question, you are advised to work throughout with 2 decimal places.)
The table below shows corresponding values ofx and y obtained in a certain experiment.
2.39
4.16
6.31
8.70
12.01
1.59
6.91
16.59
31.70
52.48
87.10
3.63
The relation connecting x and y is: y = x" where'2 and n are constants.
By drawing a suitable linear graph relating log10 xand log10 y, calculate the values of 1 and
n.
dy
X =
-
70. Obtain in the form: y = f(x), a particular solution of the differential equation:
dx
2xy, given that y = 0 when x = 0.
71. Solve the differential equation x(1 – y) = -2y given that y = 2when x = e. Hence, show that
dx
dy
y = In (2)(-
dy
72. Solve the differential equation x
dx
y(2x² + 1)(.

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