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Which of the following is the general solution of the differential equation ху" — у' — 1? а) c,х + 2с,у — 0 b) y = c, + c,-x c) y = cx + c2- d) y = c, + c,x² + e* x2 e) y = c1 + C2 ,+x

Which of the following is the general solution of the differential equation ху" — у' — 1? а) c,х + 2с,у — 0 b) y = c, + c,-x c) y = cx + c2- d) y = c, + c,x² + e* x2 e) y = c1 + C2 ,+x

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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Which of the following is the general solution of the differential equation ху" — у' — 1? a) c,x + 2c2y = 0 b) y = c, +c,-x 2 c) y = c,x + cz d) y = c1 + C2x² + e* e) y = c, + c,÷+x 2
Transcribed Image Text:Which of the following is the general solution of the differential equation ху" — у' — 1? a) c,x + 2c2y = 0 b) y = c, +c,-x 2 c) y = c,x + cz d) y = c1 + C2x² + e* e) y = c, + c,÷+x 2
Expert Solution
Step 1

The differential equation is given as

xy''-y'=1

Multiply both sides of the given differential equation by x to obtain the Cauchy Euler form

x2y''-xy'=x                                       (1)

Suppose x=ez, then

x2y''=D'(D'-1)yxy'=D'yD'=ddz

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