Explanation Given: The given differential equation is, ( t 2 − t − 2 ) 2 x ″ + ( t 2 − 4 ) x ′ − t x = 0 . Approach: A singular point x 0 of y ″ ( x ) + p ( x ) y ′ ( x ) + q ( x ) y ( x ) = 0 is a regular singular point if both ( x − x 0 ) p ( x ) and ( x − x 0 ) 2 q ( x ) are analytic at x 0 otherwise the point is irregular singular point. If a function is defined at a point x 0 , then it is analytic at the point x 0 . Calculation: Compare the given equation with the standard form to get, p ( t ) = t 2 − 4 ( t 2 − t − 2 ) 2 q ( t ) = − t ( t 2 − t − 2 ) 2 The singular points are − 1 and 2 . At t 0 = − 1 ( t − t 0 ) p ( t ) = ( t + 1 ) p ( t ) = ( t + 1 ) t + 2 ( t − 2 ) ( t + 1 ) 2 = t + 2 ( t + 1 ) ( t − 2 )

7th Edition

ISBN: 9780321977175

Author: Nagle

Publisher: PEARSON CO

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Chapter 8.6, Problem 7E

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Whether the differential equation (t2−t−2)2x″+(t2−4)x′−tx=0 has a regular singular point or an irregular singular point.

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Chapter 8.6, Problem 6E

Chapter 8.6, Problem 8E

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To state: Whether the differential equation ( t 2 − t − 2 ) 2 x ″ + ( t 2 − 4 ) x ′ − t x = 0 has a regular singular point or an irregular singular point.

Solution Summary: The author analyzes whether the differential equation (t2-t-2) has a regular or irregular singular point.

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To state:

Whether the differential equation (t2−t−2)2x″+(t2−4)x′−tx=0 has a regular singular point or an irregular singular point.

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Chapter 8 Solutions

To state: Whether the differential equation ( t 2 − t − 2 ) 2 x ″ + ( t 2 − 4 ) x ′ − t x = 0 has a regular singular point or an irregular singular point.

Solution Summary: The author analyzes whether the differential equation (t2-t-2) has a regular or irregular singular point.

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To state: Whether the differential equation (t2−t−2)2x″+(t2−4)x′−tx=0 has a regular singular point or an irregular singular point.

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Chapter 8 Solutions

To state:

Whether the differential equation (t2−t−2)2x″+(t2−4)x′−tx=0 has a regular singular point or an irregular singular point.