Explain the determaine and the Q is complete 2.8.1 Example AThe equationYKYK+1 = 2y +1(2.164)can be written asYk+1 = 2yk +1/yk.(2.165)In this form, it is easily seen that the curve in the (yk, Yk+1) plane is a hyper-bola with asymptotes yk = 0 and yk+1 = 2yk. There are no real fixed pointssince a? = 2a² + 1. Consequently, the curve does not intersect yk+1 = Yk. SeFigure 2.5.The asymptotic behavior (i.e., k → 0) is determined byYk+1 = 2yk;(2.166)the solution of which isYk = A2k,(2.167)where A is an arbitrary constant. Therefore, if we lett = A2k and z(t) = Yk;(2.168)equation (2.164) becomesz(t)z(2t) = 2z(t)² + 1,(2.169)where 2(t) has the expansionA12(t) = t + Ao +A2+t2Аз+...13(2.170)tSubstitution of this result into equation (2.169) gives, respectively, for the left-and right-hand sides4A2 + 3/2A0A1z(t)z(2t) = 2t2 + 3Aot + (Až + 5/2A1) +(2.171)17/s A3 + 5/4A0 A2 + ½A?+...t2

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where z(t) has the expansion z(t) =t+ Ao + (2.170) Substitution of this result into equation (2.169) gives, respectively, for the left- and right-hand sides z(t)z(2t) = 2t² + 3Aot + (Až + /½A1) + ¾A2 + 3½A0A1 %3D (2.171) 17/s A3 + 5/¾A0A2 +½A? t2 + +...

where z(t) has the expansion z(t) =t+ Ao + (2.170) Substitution of this result into equation (2.169) gives, respectively, for the left- and right-hand sides z(t)z(2t) = 2t² + 3Aot + (Až + /½A1) + ¾A2 + 3½A0A1 %3D (2.171) 17/s A3 + 5/¾A0A2 +½A? t2 + +...

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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6. Practice interpreting coefficients and R-squared Suppose you are interested in studying the determinants of wages. You plan to use the following model: wage — Во + Beduc + Bzеzрer+u where wage = annual salary, in thousands of dollars educ = years of education exper = years of work experience You run the ression, and obtain the ving results: wage 12+1.1 eduс + 1.5 егреr n = 200 R = 0.07 The predicted wage for an individual with 12 years of education and 1 year of experience is The predicted wage for an individual with the same years of work experience but one additional year of education (that is, 13 years) is v. The marginal effect of one extra year of education is The R of this regression indicates that v % of the variation in wage is explained by educ and exper together. Suppose you suspect that wages might be affected by the weight of each individual, either through discrimination based on weight by employers or decreased productivity, and therefore wages, brought on by an…