4. Given the equation:2ху?y' = y + -exFind the integrating factor. Choose your answer from the choices below. *IF = e2xIF = 1/exА.В.IF = e*IF — е-2хc.O D.

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Answered: 4. Given the equation: 2xy² y' = y + -…

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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What differential equation has general solution y=c1e^(5t)+c2te^(5t)?
Match column B with the correct answer on column A, write only the capital letter of the answer on the blank provided at the left side/right side of the test paper. Match from column A the solution of the differential equations on column B. Column A A. xlnx + ylny = c B. 2y = x4 + cx2 C. e(x^2) + y2 = c D. x2 = cy3 E. x2 y = 2x4 + c F. ylnx + xlny = c G. x2 (x2 + 2y2) = c H. x (y + x2) = c (y – 2x) I. xy2 – x2y + 3x2 – 2y = c J. xy3 = 2y2 + 4y + 4 + cey K. y (x2 + c) + 2 = 0 L. (y – x) (y + 3x)3 = cx3 M. x2 y = 2x2 + c N. x (y + 1) = (1 + cx) ey O. e(-x^2) + y-2 = c P. (y + x2) = c (y – 2x) Q. x2y2 + 2xy – x2 = c R. x4 = c2 (4x2 + y2) S. x2 (x+ 2y) = c T. x2 + y2 – 3xy = c Column B (x – y) (4x + y) dx + x (5x – y) dx = 0 xy3 dx + e(x^2) dy = 0 y dx + (3x – xy + 2) dy = 0 2 (2x2 + y2) dx – xy dy = 0 (x2 + y2) – xy dy = 0 (2x – 3y) dx + (2x – 3x) dy = 0 x2 yy’ = ey (x4 + 2y) dx – x dy = 0 (3x2 – 2xy + 3y2) dx = 4xydy
Match column B with the correct answer on column A, write only the capital letter of the answer on the blank provided at the left side/right side of the test paper. Match from column A the solution of the differential equations on column B. Column A A. xlnx + ylny = c B. 2y = x4 + cx2 C. e(x^2) + y2 = c D. x2 = cy3 E. x2 y = 2x4 + c F. ylnx + xlny = c G. x2 (x2 + 2y2) = c H. x (y + x2) = c (y – 2x) I. xy2 – x2y + 3x2 – 2y = c J. xy3 = 2y2 + 4y + 4 + cey K. y (x2 + c) + 2 = 0 L. (y – x) (y + 3x)3 = cx3 M. x2 y = 2x2 + c N. x (y + 1) = (1 + cx) ey O. e(-x^2) + y-2 = c P. (y + x2) = c (y – 2x) Q. x2y2 + 2xy – x2 = c R. x4 = c2 (4x2 + y2) S. x2 (x+ 2y) = c T. x2 + y2 – 3xy = c Column B (x – y) (4x + y) dx + x (5x – y) dx = 0 xy3 dx + e(x^2) dy = 0 y dx + (3x – xy + 2) dy = 0 2 (2x2 + y2) dx – xy dy = 0 (x2 + y2) – xy dy = 0 (2x – 3y) dx + (2x – 3x) dy = 0 x2 yy’ = ey (x4 + 2y) dx – x dy = 0 (3x2 – 2xy + 3y2) dx = 4xydy (1 + lnx) dx + (1 + lny) dy = 0
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Find a general solution for y'+ (1/x)y = 0, for x > 0. To receive any credit, you must use the technique for solving linear differential equations.
For the two armies X and Y, the X army is about to attack Y army which has only 7725 troops while the X army has 12440 troops. The Y army however superior military equipment’s which make each Y soldier 1.5 times as effective as X soldier. Develop a mathematical model using differential equations and explain for i) which army will win ii) Estimate how many troops of the winning army will be left at the end. iii) How long the battle will end. The kill rates of X and Y are 0.5 and 0.75 respectively.
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4. Given the equation: 2xy² y' = y + - et Find the integrating factor. Choose your answer from the choices below. * IF = e2x IF = 1/er O A. О в. IF = e* IF = e-2x %3D