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(c) given one solution of (1), y1 = e-2t and you want to produce a second unkno solution y2 by using it. Suppose the new solution has the form Y2 = u(t)y1(t) fe certain function u(t), and hence we just need to determine u(t) in order to determ Let us think about the previous part in a little different way. You %3D Y2. To find out u(t), substitute y2 (t) back into equation (1), do calculation, simp and solve for u(t) (you are supposed to have a family of choices). Last, choos suitable u(t) for y2(t) and then justify whether y1 and Y2 that you chose for fundamental set of solutions. (Compare you results to the previous part)

(c) given one solution of (1), y1 = e-2t and you want to produce a second unkno solution y2 by using it. Suppose the new solution has the form Y2 = u(t)y1(t) fe certain function u(t), and hence we just need to determine u(t) in order to determ Let us think about the previous part in a little different way. You %3D Y2. To find out u(t), substitute y2 (t) back into equation (1), do calculation, simp and solve for u(t) (you are supposed to have a family of choices). Last, choos suitable u(t) for y2(t) and then justify whether y1 and Y2 that you chose for fundamental set of solutions. (Compare you results to the previous part)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let us think about the previous part in a little different way. You are -2t and you want to produce a second unknown u(t)y1(t) for a certain function u(t), and hence we just need to determine u(t) in order to determine given one solution of (1), yi = solution y2 by using it. Suppose the new solution has the form y2 Y2. To find out u(t), substitute y2(t) back into equation (1), do calculation, simplify, and solve for u(t) (you are supposed to have a family of choices). Last, choose a suitable u(t) for y2(t) and then justify whether y1 and Y2 that you chose form a fundamental set of solutions. (Compare you results to the previous part)
Transcribed Image Text:Let us think about the previous part in a little different way. You are -2t and you want to produce a second unknown u(t)y1(t) for a certain function u(t), and hence we just need to determine u(t) in order to determine given one solution of (1), yi = solution y2 by using it. Suppose the new solution has the form y2 Y2. To find out u(t), substitute y2(t) back into equation (1), do calculation, simplify, and solve for u(t) (you are supposed to have a family of choices). Last, choose a suitable u(t) for y2(t) and then justify whether y1 and Y2 that you chose form a fundamental set of solutions. (Compare you results to the previous part)
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