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Consider the second-order differential equation for y (т — 1)}"(х) — ху (г) + у(х) — 0 -- of which a solution y(x) = exp(x) is given. • Find via order-reduction a second linearly independent solution of the given differential equation. • What for a kind of point is x = 1 ? Proof your statement. • Why do the solutions of the differential equation do not have a singu- larity in x = 1 ?

Consider the second-order differential equation for y (т — 1)}"(х) — ху (г) + у(х) — 0 -- of which a solution y(x) = exp(x) is given. • Find via order-reduction a second linearly independent solution of the given differential equation. • What for a kind of point is x = 1 ? Proof your statement. • Why do the solutions of the differential equation do not have a singu- larity in x = 1 ?

Advanced Engineering Mathematics
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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Consider the second-order differential equation for y (т — 1)}"(х) — ху (г) + у(х) — 0 -- of which a solution y(x) = exp(x) is given. • Find via order-reduction a second linearly independent solution of the given differential equation. • What for a kind of point is x = 1 ? Proof your statement. • Why do the solutions of the differential equation do not have a singu- larity in x = 1 ?
Transcribed Image Text:Consider the second-order differential equation for y (т — 1)}"(х) — ху (г) + у(х) — 0 -- of which a solution y(x) = exp(x) is given. • Find via order-reduction a second linearly independent solution of the given differential equation. • What for a kind of point is x = 1 ? Proof your statement. • Why do the solutions of the differential equation do not have a singu- larity in x = 1 ?
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