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(b). t²y" + 2ty' - 2y = 0, t>0; y₁(t) = = t Assume that y2 = v(t)y₁, using above approach with p(t) = 2/t, we have tv" + (2 + 2)v' = 0 let u = v' =0 t du = -4u dt 1 dt t ¼ du = -4½ at In |u| = −4ln|t| +C, -4ln|t|+C, u = ct−4 v = √ udt = c₁t³ ³ + c₂ y2 = (c₁t-³ + c2)t

(b). t²y" + 2ty' - 2y = 0, t>0; y₁(t) = = t Assume that y2 = v(t)y₁, using above approach with p(t) = 2/t, we have tv" + (2 + 2)v' = 0 let u = v' =0 t du = -4u dt 1 dt t ¼ du = -4½ at In |u| = −4ln|t| +C, -4ln|t|+C, u = ct−4 v = √ udt = c₁t³ ³ + c₂ y2 = (c₁t-³ + c2)t

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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(b). t²y" + 2ty' - 2y = 0, t>0; y₁(t) = = t Assume that y2 = v(t)y₁, using above approach with p(t) = 2/t, we have tv" + (2 + 2)v' = 0 let u = v' =0 t du = -4u dt 1 dt t ¼ du = -4½ at In |u| = −4ln|t| +C, -4ln|t|+C, u = ct−4 v = √ udt = c₁t³ ³ + c₂ y2 = (c₁t-³ + c2)t
Transcribed Image Text:(b). t²y" + 2ty' - 2y = 0, t>0; y₁(t) = = t Assume that y2 = v(t)y₁, using above approach with p(t) = 2/t, we have tv" + (2 + 2)v' = 0 let u = v' =0 t du = -4u dt 1 dt t ¼ du = -4½ at In |u| = −4ln|t| +C, -4ln|t|+C, u = ct−4 v = √ udt = c₁t³ ³ + c₂ y2 = (c₁t-³ + c2)t
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