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Find the general solution of the differential equation. y(4) – 6y(3) + 9y'" = 0 ... y(x) =

Find the general solution of the differential equation. y(4) – 6y(3) + 9y'" = 0 ... y(x) =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the general solution of the differential equation. y(4) – 6y(3) + 9y'" = 0 ... y(x) =
Transcribed Image Text:Find the general solution of the differential equation. y(4) – 6y(3) + 9y'" = 0 ... y(x) =
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A third-order Euler equation is one of the form axy' + bx²y'" + 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 + (b - За)— d?y + (c - b+ 2a) + ky = 0 dv? dy dv a- dv Make the substitution v = In x to find the general solution of x°y'"' + 11x?y" + 9xy' = 0 for x > 0. y(x) =
Transcribed Image Text:A third-order Euler equation is one of the form axy' + bx²y'" + 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 + (b - За)— d?y + (c - b+ 2a) + ky = 0 dv? dy dv a- dv Make the substitution v = In x to find the general solution of x°y'"' + 11x?y" + 9xy' = 0 for x > 0. y(x) =
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