Determine a Cauchy-Euler equation of minimum possible order with real coefficients if it is known that m = 5 and m = -3i are two of the roots of its auxiliary equation. You may find it helpful that a third-order Cauchy-Euler equation of the form ax y" + bx² y" + cxy + dy = 0 has the following auxiliary equation: am? + (b — За)т? + (2а — b + c)m + d %3D 0.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter1: Equations And Inequalities
Section1.CR: Chapter Review
Problem 68E: Determine the number and nature of the roots of the equation in Exercise 67. Calculate the...
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Determine a Cauchy-Euler equation of minimum possible
order with real coefficients if it is known that m = 5 and
m = -3i are two of the roots of its auxiliary equation.
You may find it helpful that a third-order Cauchy-Euler
equation of the form ax'y" + bx²y" + cxy + dy = 0 has
the following auxiliary equation:
ат* + (b — За)т? + (2а — b + с)т + d %3D 0.
Transcribed Image Text:Determine a Cauchy-Euler equation of minimum possible order with real coefficients if it is known that m = 5 and m = -3i are two of the roots of its auxiliary equation. You may find it helpful that a third-order Cauchy-Euler equation of the form ax'y" + bx²y" + cxy + dy = 0 has the following auxiliary equation: ат* + (b — За)т? + (2а — b + с)т + d %3D 0.
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