The solution of the differential equationx'y" + 3xy' + 6y = 0 (x > 0)is the functiony(x) = C y:(X) + C; y:(X).Find y,(x) and y (x). Also, find the constants C, and C; if y(1) = - 1, y'(1) = 2.O A. y,0) = x' cos (V5 In(x), y,«) = x" sin (V5 In(x)), C, = - 1, C, =-V5B. y,(x) = x' cos (V5 In(x)), y:(x) = x' sin (V5 In(x)), C, = - 1, C; =COSV51O C y,() = x cos (V5 In(x), y;(x) = x sin (V3 In(x), c, - - 1, C =V5O D. y,(X) = x cos (V3 In(x), y,(x) = x sin (V3 In(x), C, = - 1, C, •

Given differential equation is Cauchy-Euler differential equation of second order with variable…

The solution of the differential equation x'y" + 3xy' + 6y = 0 (x > 0) is the function y(x) = C, y;(x) + C2 y:(x). Find y,(x) and y:(x). Also, find the constants C, and C; if y(1) = - 1, y(1) = 2. O A. y,) = x' cos (V5 In(x), y;0«) = x' sin (V3 In(x), c, - - 1, C, = O B. y,() = x' cos (V3 In(x), y:0x) = x' sin (V3 In(x), c, - - 1, G; = - O C. y,(x) = x cos (V5 In(x)), y:(x) = x sin(v3 In(x)), C, = - 1, C; = - O D. y,(x) = x cos (V5 In(x»), y,x) = x sin (V3 In(x), C, = - 1, C; =

The solution of the differential equation x'y" + 3xy' + 6y = 0 (x > 0) is the function y(x) = C, y;(x) + C2 y:(x). Find y,(x) and y:(x). Also, find the constants C, and C; if y(1) = - 1, y(1) = 2. O A. y,) = x' cos (V5 In(x), y;0«) = x' sin (V3 In(x), c, - - 1, C, = O B. y,() = x' cos (V3 In(x), y:0x) = x' sin (V3 In(x), c, - - 1, G; = - O C. y,(x) = x cos (V5 In(x)), y:(x) = x sin(v3 In(x)), C, = - 1, C; = - O D. y,(x) = x cos (V5 In(x»), y,x) = x sin (V3 In(x), C, = - 1, C; =

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The solution of the differential equation
x'y" + 3xy' + 6y = 0 (x > 0)
is the function
y(x) = C y:(X) + C; y:(X).
Find y,(x) and y (x). Also, find the constants C, and C; if y(1) = - 1, y'(1) = 2.
O A. y,0) = x' cos (V5 In(x), y,«) = x" sin (V5 In(x)), C, = - 1, C, =-
V5
B. y,(x) = x' cos (V5 In(x)), y:(x) = x' sin (V5 In(x)), C, = - 1, C; =
COS
V5
1
O C y,() = x cos (V5 In(x), y;(x) = x sin (V3 In(x), c, - - 1, C =
V5
O D. y,(X) = x cos (V3 In(x), y,(x) = x sin (V3 In(x), C, = - 1, C, •

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