HW 24-6.2:Properties of LogarithmsScore: 2/102/10 answeredQuestion 10<>If In a= 2, In b = 3, and In c = 5, evaluate the following:a4(a) In(b) In Va*b'c!C.Question Help: D VideoSubmit QuestionJump to Answer

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Answered: If In a 2, In b = 3, and In c = 5,…

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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In this exercise we consider finding the general solution of the first order linear equation y' - 6xy = 0. This equation has an ordinary point at x = 0 and therefore has a power series solution in the form an = 0 NOTE that ao is an arbitrary constant and a a2k+1 even terms as We learned how to easily solve problems like this in several different ways but here we want to consider the power series method. (1) Insert the formal power series into the differential equation and derive the recurrence relation an-2 for n = 1, 2, .. a2 ao 0. The recurrence relation then implies that = 0 for k = 0, 1, 2, . Thus we see that the solution series can be written using only the = Y 3 a2k 9n/(n+4) = Y ao, a4 = 18/4 ao (2) Use the recurrence relation to find the first few coefficients in terms of y = ao ∞ n=0 k=0 = n Anxn ∞ k=0 a zk x ² k ao, a6 (3) Write out a few more terms if needed but try to guess the pattern for the general term ao for all k = 18/4 1, 2, . (4) Therefore the general solution, with…

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If In a 2, In b = 3, and In c = 5, evaluate the following: at (a) In 64c3 (b) ln Vaºb'c!