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(c). ty" +3ty' + y = 0, t>0; y₁(t) = t−1 Assume that y2 = v(t)y₁, using above approach with p(t) = 3/t, we have let u = = v' 1-10" + ( − 1 1/2 + 1/320² = 0 +2 x² + 1 = 0 -u u' t 1 1 -du = dt In |u| = − In|t|+C, u = ct-1 == – v = Y2 = udt = c₁ In |t| + c₂ © 1½ (c₁ In |t| + C2) t

(c). ty" +3ty' + y = 0, t>0; y₁(t) = t−1 Assume that y2 = v(t)y₁, using above approach with p(t) = 3/t, we have let u = = v' 1-10" + ( − 1 1/2 + 1/320² = 0 +2 x² + 1 = 0 -u u' t 1 1 -du = dt In |u| = − In|t|+C, u = ct-1 == – v = Y2 = udt = c₁ In |t| + c₂ © 1½ (c₁ In |t| + 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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In each of the following problems, use the method of reduction of order to find a sec-

ond solution of the given differential equation. (Can you show steps)

(c). ty" +3ty' + y = 0, t>0; y₁(t) = t−1 Assume that y2 = v(t)y₁, using above approach with p(t) = 3/t, we have let u = = v' 1-10" + ( − 1 1/2 + 1/320² = 0 +2 x² + 1 = 0 -u u' t 1 1 -du = dt In |u| = − In|t|+C, u = ct-1 == – v = Y2 = udt = c₁ In |t| + c₂ © 1½ (c₁ In |t| + C2) t
Transcribed Image Text:(c). ty" +3ty' + y = 0, t>0; y₁(t) = t−1 Assume that y2 = v(t)y₁, using above approach with p(t) = 3/t, we have let u = = v' 1-10" + ( − 1 1/2 + 1/320² = 0 +2 x² + 1 = 0 -u u' t 1 1 -du = dt In |u| = − In|t|+C, u = ct-1 == – v = Y2 = udt = c₁ In |t| + c₂ © 1½ (c₁ In |t| + C2) t
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