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Calculus / Fundamentals of Differential Equations 8 / Chapter 4.7 / Problem 51E

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

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th-order equation to a homogeneous linear (n-1)th-order

Chapter 4, Problem 51E

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QUESTION:

PROBLEM 51EThe reduction of order procedure can be used more generally to reduce a homogeneous linear nth-order equation to a homogeneous linear (n-1)th-order equation. For the equation which has f(t) = et as a solution, use the substitution y(t) = v(t)f(t) to reduce this third-order equation to a homogeneous linear second-order equation in the variable w = v’.

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QUESTION:

PROBLEM 51EThe reduction of order procedure can be used more generally to reduce a homogeneous linear nth-order equation to a homogeneous linear (n-1)th-order equation. For the equation which has f(t) = et as a solution, use the substitution y(t) = v(t)f(t) to reduce this third-order equation to a homogeneous linear second-order equation in the variable w = v’.

ANSWER:

Solution In this question, for the equation , where is the solution Using substitution we have to reduce this third order equation t

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