Explanation The given differential equation is ( x 2 + x − 6 ) y ″ + ( x + 3 ) y ′ + ( x − 2 ) y = 0 . Writing the given differential equation in the form y ″ + a 1 ( x ) a 2 ( x ) y ′ + a 0 ( x ) a 2 ( x ) y = 0 gives y ″ + ( x + 3 ) ( x + 3 ) ( x − 2 ) y ′ + ( x − 2 ) ( x + 3 ) ( x − 2 ) y = 0 On comparison, the values are obtained as follows: a 0 ( x ) = ( x − 2 ) a 1 ( x ) = ( x + 3 ) a 2 ( x ) = ( x + 3 ) ( x − 2 ) Now, singular point is obtained by equating a 2 ( x ) = ( x + 3 ) ( x − 2 ) to zero. So, singular point are obtained as x = 2 , − 3 . Also, a singular point x = x 0 is said to be a regular singular point of the differential equation y ″ + a 1 ( x ) a 2 ( x ) y ′ + a 0 ( x ) a 2 ( x ) y = 0 if the functions p ( x ) = ( x − x 0 ) a 1 ( x ) a 2 ( x ) and q ( x ) = ( x − x 0 ) 2 a 0 ( x ) a 2 ( x ) are both analytic at x 0 . A singular point that is not regular is said to be an irregular singular point of the equation

Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

11th Edition

ISBN: 9781305965737

Author: Dennis G. Zill

Publisher: Brooks Cole

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Chapter 6.3, Problem 7E

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The singular points of the differential equation (x2+x−6)y″+(x+3)y′+(x−2)y=0 and classify them as regular or irregular.

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The singular points of the differential equation ( x 2 + x − 6 ) y ″ + ( x + 3 ) y ′ + ( x − 2 ) y = 0 and classify them as regular or irregular.

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The singular points of the differential equation (x2+x−6)y″+(x+3)y′+(x−2)y=0 and classify them as regular or irregular.

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