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

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

Advanced Engineering Mathematics
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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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)(.
Transcribed Image Text: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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