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A third-order Euler equation is one of the form ax°y"' + bx-y" + cxy' + ky = 0, where a, b, c, and k are constants. If x> 0, then the substitution v = In x transforms the equation into the constant coefficient linear equation below, with independent variable v. + (b - За)- dv dy + ky = 0 dv + (c-b+2a)- a dv? Make the substitution v = In x to find the general solution of 2x°y"" + 13xy" + 9xy' = 0 for x>0. y(x) =O

A third-order Euler equation is one of the form ax°y"' + bx-y" + cxy' + ky = 0, where a, b, c, and k are constants. If x> 0, then the substitution v = In x transforms the equation into the constant coefficient linear equation below, with independent variable v. + (b - За)- dv dy + ky = 0 dv + (c-b+2a)- a dv? Make the substitution v = In x to find the general solution of 2x°y"" + 13xy" + 9xy' = 0 for x>0. y(x) =O

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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A third-order Euler equation is one of the form ax°y"" + bx y" + cxy' + ky = 0, where a, b, c, and k are constants. If x> 0, then the substitution v = In x transforms the equation into the constant coefficient linear equation below, with independent variable v. + (b - 3a)- dv2 dy + ky = 0 dv + (c -b+2a): a dv3 Make the substitution v = In x to find the general solution of 2x°y"' + 13xy" + 9xy' = 0 for x> 0. y(x) =
Transcribed Image Text:A third-order Euler equation is one of the form ax°y"" + bx y" + cxy' + ky = 0, where a, b, c, and k are constants. If x> 0, then the substitution v = In x transforms the equation into the constant coefficient linear equation below, with independent variable v. + (b - 3a)- dv2 dy + ky = 0 dv + (c -b+2a): a dv3 Make the substitution v = In x to find the general solution of 2x°y"' + 13xy" + 9xy' = 0 for x> 0. y(x) =
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