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In Problem 25 it was shown that the substitution x = ln(t) transforms dy dy the Euler equation t + at + By = 0 into the second-order dt? dt linear differential equation with constant coefficients dy + (a – 1) dy + By = 0. Use this result to find the general solution dx dx? of the equation ty" – 4ty – 14y = 0 for t > 0. NOTE: Use c, and cz for the constants of integration. y(t) =

In Problem 25 it was shown that the substitution x = ln(t) transforms dy dy the Euler equation t + at + By = 0 into the second-order dt? dt linear differential equation with constant coefficients dy + (a – 1) dy + By = 0. Use this result to find the general solution dx dx? of the equation ty" – 4ty – 14y = 0 for t > 0. NOTE: Use c, and cz for the constants of integration. y(t) =

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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In Problem 25 it was shown that the substitution x = ln(t) transforms dy dy the Euler equation t + at + By = 0 into the second-order dt? dt linear differential equation with constant coefficients dy + (a – 1) dy + By = 0. Use this result to find the general solution dx dx? of the equation ty" – 4ty – 14y = 0 for t > 0. NOTE: Use c, and cz for the constants of integration. y(t) =
Transcribed Image Text:In Problem 25 it was shown that the substitution x = ln(t) transforms dy dy the Euler equation t + at + By = 0 into the second-order dt? dt linear differential equation with constant coefficients dy + (a – 1) dy + By = 0. Use this result to find the general solution dx dx? of the equation ty" – 4ty – 14y = 0 for t > 0. NOTE: Use c, and cz for the constants of integration. y(t) =
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