10. Consider the solution of x'y" + 3x? y' -15x y = nxP+1 (x+0), dy Where y' and y" are respectively and dy; n>0 and B is a constant parameter to be dx determined. a) Find a proper value of 7, such that the variable x can be chosen from -0 to o with x+ 0, avoid the solution of y = c x , and make the solution y=y(x) remain real valued? b) By choosing proper values of B. you may obtain pairs of real-valued solutions, check if they are LI. c) If x = 1, we have y(1) = 0 and y'(1) = 6, determine your final solution. d) Check the stability of the solution, list the unstable conditions.
10. Consider the solution of x'y" + 3x? y' -15x y = nxP+1 (x+0), dy Where y' and y" are respectively and dy; n>0 and B is a constant parameter to be dx determined. a) Find a proper value of 7, such that the variable x can be chosen from -0 to o with x+ 0, avoid the solution of y = c x , and make the solution y=y(x) remain real valued? b) By choosing proper values of B. you may obtain pairs of real-valued solutions, check if they are LI. c) If x = 1, we have y(1) = 0 and y'(1) = 6, determine your final solution. d) Check the stability of the solution, list the unstable conditions.
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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part d
Transcribed Image Text:10. Consider the solution of x'y" + 3x? y' -15x y = nxP+1 (x+0),
dy
Where y' and y" are respectively
and dy; n>0 and B is a constant parameter to be
dx
determined.
a) Find a proper value of 7, such that the variable x can be chosen from -0 to o with x+
0, avoid the solution of y = c x , and make the solution y=y(x) remain real valued?
b) By choosing proper values of B. you may obtain pairs of real-valued solutions, check if
they are LI.
c) If x = 1, we have y(1) = 0 and y'(1) = 6, determine your final solution.
d) Check the stability of the solution, list the unstable conditions.
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