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Consider the second order differential equation dy Answer: dx Note. Your answers should be functions of x. (a) We observe that the function y itself does not appear in the given equation. By considering the differential equation as a first order differential equation in the function v = dy dx find v. (b) Use the result of (a) to find y. V= +C₁ where C₁ is an arbitrary constant. Answer: y = xy" + 4y = -8x =0+ +C₁+C₂, where C₁ and C₂ are arbitrary constants. x-12 Note. Your answers should be functions of x.

Consider the second order differential equation dy Answer: dx Note. Your answers should be functions of x. (a) We observe that the function y itself does not appear in the given equation. By considering the differential equation as a first order differential equation in the function v = dy dx find v. (b) Use the result of (a) to find y. V= +C₁ where C₁ is an arbitrary constant. Answer: y = xy" + 4y = -8x =0+ +C₁+C₂, where C₁ and C₂ are arbitrary constants. x-12 Note. Your answers should be functions of x.

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 1CR
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Consider the second order differential equation dy Answer: dx Note. Your answers should be functions of x. (a) We observe that the function y itself does not appear in the given equation. By considering the differential equation as a first order differential equation in the function v dy = find v. dx' xy" + 4y = -8x =υ= +C₁ where C₁ is an arbitrary constant. (b) Use the result of (a) to find y. Answer: y = Note. Your answers should be functions of x. +C₁ +C2, where C₁ and C₂ are arbitrary constants. -12
Transcribed Image Text:Consider the second order differential equation dy Answer: dx Note. Your answers should be functions of x. (a) We observe that the function y itself does not appear in the given equation. By considering the differential equation as a first order differential equation in the function v dy = find v. dx' xy" + 4y = -8x =υ= +C₁ where C₁ is an arbitrary constant. (b) Use the result of (a) to find y. Answer: y = Note. Your answers should be functions of x. +C₁ +C2, where C₁ and C₂ are arbitrary constants. -12
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