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If x = a +0 is a singular point of a second-order linear differential equation, then the substitution t=x-a transforms it into a differential equation having t=0 as a singular point. We then attribute to the original equation at x = a the behavior of the new equation at t= 0. Classify (as regular or irregular) the singular points of the differential equation. (5-x)y" + xy' +6x²y = 0

If x = a +0 is a singular point of a second-order linear differential equation, then the substitution t=x-a transforms it into a differential equation having t=0 as a singular point. We then attribute to the original equation at x = a the behavior of the new equation at t= 0. Classify (as regular or irregular) the singular points of the differential equation. (5-x)y" + xy' +6x²y = 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.CR: Chapter 11 Review
Problem 33CR
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If x = a #0 is a singular point of a second-order linear differential equation, then the substitution t = x - a transforms it into a differential equation having t=0 as a singular point. We then attribute to the original equation at x = a the behavior of the new equation at t= 0. Classify (as regular or irregular) the singular points of the differential equation. (5-x)y" + xy' + 6x²y=0 Identify any regular singular points. Select the correct answer below and fill in any answer boxes within your choice. OA. The differential equation has the regular singular point(s)x= (Simplify your answer. Use a comma to separate answers as needed.) O B. The differential equation has no regular singular points. Identify any irregular singular points. Select the correct answer below and fill in any answer boxes within your choice. O A. The differential equation has the irregular singular point(s) x = (Simplify your answer. Use a comma to separate answers as needed.) B. The differential equation has no irregular singular points.
Transcribed Image Text:If x = a #0 is a singular point of a second-order linear differential equation, then the substitution t = x - a transforms it into a differential equation having t=0 as a singular point. We then attribute to the original equation at x = a the behavior of the new equation at t= 0. Classify (as regular or irregular) the singular points of the differential equation. (5-x)y" + xy' + 6x²y=0 Identify any regular singular points. Select the correct answer below and fill in any answer boxes within your choice. OA. The differential equation has the regular singular point(s)x= (Simplify your answer. Use a comma to separate answers as needed.) O B. The differential equation has no regular singular points. Identify any irregular singular points. Select the correct answer below and fill in any answer boxes within your choice. O A. The differential equation has the irregular singular point(s) x = (Simplify your answer. Use a comma to separate answers as needed.) B. The differential equation has no irregular singular points.
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