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hird-order Euler equation is one of the form ax y"" + bxʻy" + cxy' + ky = 0, where a, b, c, and k are constant n the substitution v= In x transforms the equation into the constant coefficient linear equation below, with inc iable v. d°y + (b- За) dv d?y + (с-b+ 2a) dv? dy + ky = 0 a- ke the substitution v = In x to find the general solution of x°y'"' + 9x0.

hird-order Euler equation is one of the form ax y"" + bxʻy" + cxy' + ky = 0, where a, b, c, and k are constant n the substitution v= In x transforms the equation into the constant coefficient linear equation below, with inc iable v. d°y + (b- За) dv d?y + (с-b+ 2a) dv? dy + ky = 0 a- ke the substitution v = In x to find the general solution of x°y'"' + 9x0.

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 22E
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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. d°y d²y + (с -b+2a)- dv? dy + ky = 0 dv a + (b - За)- 3 dv Make the substitution v = In x to find the general solution of x y"" + 9xy'" + 19xy' + 8y = 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. d°y d²y + (с -b+2a)- dv? dy + ky = 0 dv a + (b - За)- 3 dv Make the substitution v = In x to find the general solution of x y"" + 9xy'" + 19xy' + 8y = 0 for x> 0. y(x) =|
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