5. Consider the differential equation (x - 1)y" - xy + y = 0, x > 1' a. Do f(x) = e* and g(x) = x² form a fundamental set of solutions to the differential equation on x > 1? State why or why not. If so, write the general solution. b. Do f(x) = et and g(x) = 4e form a fundamental set of solutions to the differential equation on x > 1? State why or why not. If so, write the general solution.
5. Consider the differential equation (x - 1)y" - xy + y = 0, x > 1' a. Do f(x) = e* and g(x) = x² form a fundamental set of solutions to the differential equation on x > 1? State why or why not. If so, write the general solution. b. Do f(x) = et and g(x) = 4e form a fundamental set of solutions to the differential equation on x > 1? State why or why not. If so, write the general solution.
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:c. Do f(x) = e" and g(x) = x form a fundamental set of solutions to the differential
equation on x > 1? State why or why not. If so, write the general solution.
Transcribed Image Text:5. Consider the differential equation (x - 1)y" - xy + y = 0, x > 1'
=
a. Do f(x) = e" and g(x) = x² form a fundamental set of solutions to the differential
equation on x > 1? State why or why not. If so, write the general solution.
b. Do f(x) = e¹ and g(x) = 4e* form a fundamental set of solutions to the differential
equation on x > 1? State why or why not. If so, write the general solution.
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