The solution of the differential equation x*y" - 2xy' + 6y = 0 (x > 0) is the function y(x) = C; y;(x) + C2 y2(x). Find y,(x) and y,(x). Also, find the constants C, and C, if y(1) = - 1, y'(1) = 1. VI3 In(x), y(x) = x3/2sin V15 VIS In(x)|, C, = - 1, C2 . 2 O A. y,(x) = x3/2cos V15 In(x), y2(x) = x32sin /15 In(x) 2 B. y;(x) = x3/2cos C, = -1, C2 = - [3 O C. y,(x) = x3/2cos 2 In(x), y2(x) = x3/2sin 1(x)|, C, = - 1, Cz =- VI3 O D. y;(x) = x³2cos VI3 5 In(x) , y(x) = x3/2sin - In(x) ), C, = - 1, C2 =. [3 n Jen
The solution of the differential equation x*y" - 2xy' + 6y = 0 (x > 0) is the function y(x) = C; y;(x) + C2 y2(x). Find y,(x) and y,(x). Also, find the constants C, and C, if y(1) = - 1, y'(1) = 1. VI3 In(x), y(x) = x3/2sin V15 VIS In(x)|, C, = - 1, C2 . 2 O A. y,(x) = x3/2cos V15 In(x), y2(x) = x32sin /15 In(x) 2 B. y;(x) = x3/2cos C, = -1, C2 = - [3 O C. y,(x) = x3/2cos 2 In(x), y2(x) = x3/2sin 1(x)|, C, = - 1, Cz =- VI3 O D. y;(x) = x³2cos VI3 5 In(x) , y(x) = x3/2sin - In(x) ), C, = - 1, C2 =. [3 n Jen
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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Transcribed Image Text:The solution of the differential equation
x²y" - 2xy' + 6y = 0 (x > 0)
is the function
y(x) = C; y,(x) + C Y2(X).
Find y,(x) and y,(x). Also, find the constants C, and C, if y(1) = - 1, y'(1) = 1.
VI3
VI5
O A. y,(x) = x3/2cos
In(x), y-(x) = x3/2sin
In(x)|, C, = - 1, C2 = 1
3
V13
In(x), y2(x) = x³3/2sin
V15 In(x), C, = -1, C2 = - -
B. y,(x) = x3/2cos
2
VI5
In(x), y2(x) = x3/2sin
O C. y,(x) = x3/2cos
In(x)
= - 1, C
VI3
D. y,(x) = x3/2cos
In(x) , y2(x) = x3/2sin
In(x), C, = - 1, C2
n Jen
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