9ac 30%9.4.5.6.7.8.ProblemsIn each of Problems 1 through 8, solve the given differential equation.x²1. y'==2.3.38 CHAPTER 2 First-Order Differential Equationsyy' + y² sin x = 0y' = cos(x) cos² (2y)xy' = (1 - y2) 1/2x-e-*38 38 3863dydxdydxdydxdydx====1+ y²al%y + ey1-2yy' ==1+3x²Зу2 — буy(0) = 1yIn each of Problems 9 through 16:a. Find the solution of the given initial value problem in explicitform.Gb. Plot the graph of the solution.c. Determine (at least approximately) the interval in which thesolution is defined.y'= (1-2x) y²,y(0) = -1/610.y'=(1-2x)/y, y(1) = −211. xdx+ye*dy = 0, y(0) = 112. dr/d0 = r²/0, r(1) = 213. y'=xy³(1+x²)-1/², y(0) = 1 = (14. y'= 2x/(1+2y), y(2) = 0= (ut.x)\ li seussed brill 23. Solve the equation o15. y' = (3x²-e¹)/(2y-5), y(0) = 1Inilgenotihad to noirulosa aloc= (no16. sin(2x) dx + cos(3y) dy = 0, y(π/2) = π/3Some of the results requested in Problems 17 through 22 can beobtained either by solving the given equations analytically or byplotting numerically generated approximations to the solutions. Tryto form an opinion about the advantages and disadvantages of eachapproach.150TOG 17. Solve the initial value problemand determine the interval in which the solution is valid.Hint: To find the interval of definition, look for points where theintegral curve has a vertical tangent.G 18. Solve the initial value problem3x²3y² - 4'y' =y(1) = 0ow (TS) brus (OS)G 19.and determine the interval in which the solution is valid.Hint: To find the interval of definition, look for points where theintegral curve has a vertical tangent.19. Solve the initial value problemy' = 2y² + xy², y(0) = 1and determine where the solution attains its minimum value.G 20. Solve the initial value problem2- et3+2yy(0) = 0y' ==and determine where the solution attains its maximum value.G21. Consider the initial value problemty(4-y)y' =y(0) = yo.3a. Determine how the behavior of the solution as t increasesdepends on the initial value yo.b. Suppose that yo= 0.5. Find the time T at which the solutionfirst reaches the value 3.98.G 22. Consider the initial value problemdQdtty(4- y)1+ty' =y(0) = yo > 0. Claa.Determine how the solution behaves as t →∞.b. If yo= 2, find the time T at which the solution first reachesthe value 3.99.c. Find the range of initial values for which the solution lies inthe interval 3.99

In this question we have to solve the given differential eq. in the explicit form. Let's solve and…

In each of Problems 9 through 16: a. Find the solution of the given initial value problem in explicit 9. 10. form. Gb. Plot the graph of the solution. c. Determine (at least approximately) the interval in which the solution is defined. y'=(1-2x) y2, y(0) = -1/6 y'=(1-2)( WODY

In each of Problems 9 through 16: a. Find the solution of the given initial value problem in explicit 9. 10. form. Gb. Plot the graph of the solution. c. Determine (at least approximately) the interval in which the solution is defined. y'=(1-2x) y2, y(0) = -1/6 y'=(1-2)( WODY

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter5: Sensitivity Analysis: An Applied Approach

Section5.2: The Computer And Sensitivity Analysis

Problem 1P

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