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The point x = 0 is a regular singular point of the given differential equation. 2xy" + 7y' + xy = 0

The point x = 0 is a regular singular point of the given differential equation. 2xy" + 7y' + xy = 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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16** +. The point x = O is a regular singular point of the given differential equation. 2xy" + 7y' + ху %3D 0 + r Substitute y = C into the differential equation and collect terms to rewrite as a single power series. n=0 00 2ху" + 7y' + ху %3 1 + k +r - 1 k=2 Show that the indicial rootsr of the singularity do not differ by an integer. (List the indicial roots below as a comma-separated list.) r = Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on (0, 0). 1 2 - X -) + c<(1- 1 1 y = Cqx-5/2(1 x² 24 + + + 2112 - 16 1152 **..) + c_(1 - .) + c2(1 - 1 .) + c<(1 + ? 1 2 1 1 y = C,x=5/2(1 + 1 + 936 4 + 4 24 18 Oy = C;x-5/2(1 1x? + 1 + x² + 18 936 1152 1 1 1. 2 1 y = C;x=5/2(1 2 + 4 + %3D - 18 936 2 24 :) 1 1 y = C,x-5/2(1 ,2 + + C, x² 16 1 x4 + . . . + 1 + 1152 24 2112 ) Need Help? Read It Watch It
Transcribed Image Text:16** +. The point x = O is a regular singular point of the given differential equation. 2xy" + 7y' + ху %3D 0 + r Substitute y = C into the differential equation and collect terms to rewrite as a single power series. n=0 00 2ху" + 7y' + ху %3 1 + k +r - 1 k=2 Show that the indicial rootsr of the singularity do not differ by an integer. (List the indicial roots below as a comma-separated list.) r = Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on (0, 0). 1 2 - X -) + c<(1- 1 1 y = Cqx-5/2(1 x² 24 + + + 2112 - 16 1152 **..) + c_(1 - .) + c2(1 - 1 .) + c<(1 + ? 1 2 1 1 y = C,x=5/2(1 + 1 + 936 4 + 4 24 18 Oy = C;x-5/2(1 1x? + 1 + x² + 18 936 1152 1 1 1. 2 1 y = C;x=5/2(1 2 + 4 + %3D - 18 936 2 24 :) 1 1 y = C,x-5/2(1 ,2 + + C, x² 16 1 x4 + . . . + 1 + 1152 24 2112 ) Need Help? Read It Watch It
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