Explanation Formula used: The Wronskian of any two solutions y 1 and y 2 to the equation y ″ ( t ) + p y ′ ( t ) + q y ( t ) = 0 on ( a , b ) is given by Abel’s formula W [ y 1 , y 2 ] ( t ) = C exp { − ∫ t 0 t p ( τ ) d τ } . Calculation: The given differential equation is, t y ″ + ( t − 1 ) y ′ + 3 y = 0 . Divide by t and simplify as, y ″ + ( t − 1 t ) y ′ + 3 t y = 0 y ″ + ( 1 − 1 t ) y ′ + 3 t y = 0 Comparing y ″ + ( 1 − 1 t ) y ′ + 3 t y = 0 with the general form y ″ ( t ) + p y ′ ( t ) + q y ( t ) = 0 gives p = 1 − 1 t

Fundamentals of Differential Equations (9th Edition)

9th Edition

ISBN: 9780321977069

Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Publisher: PEARSON

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Chapter 4.7, Problem 33E

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The Wronskian of two solutions on (0,∞) to ty″+(t−1)y′+3y=0.

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Chapter 4.7, Problem 32E

Chapter 4.7, Problem 34E

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Fundamentals of Differential Equations (9th Edition)

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The Wronskian of two solutions on ( 0 , ∞ ) to t y ″ + ( t − 1 ) y ′ + 3 y = 0 .

Solution Summary: The author explains how the Wronskian of two solutions on (0,infty) is divided by t and simplified by Abel’s formula.

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The Wronskian of two solutions on (0,∞) to ty″+(t−1)y′+3y=0.

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