Can you explain further how you go from (e^2t*e^2C)/2 to (e^2t/2)e^2t? I feel like e^2C was lost somehow.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Can you explain further how you go from (e^2t*e^2C)/2 to (e^2t/2)e^2t? I feel like e^2C was lost somehow.

Taking exponential on both sides,
2y - 15
e2t+20₁
2y - 15 e2te20₁
2y = e²te2 +15.
+35)
y= 2²e²¹ +7.5 (= c)
2t
y = C'e²t +7.5
That is, y(t) = C'e²t +7.5.
Transcribed Image Text:Taking exponential on both sides, 2y - 15 e2t+20₁ 2y - 15 e2te20₁ 2y = e²te2 +15. +35) y= 2²e²¹ +7.5 (= c) 2t y = C'e²t +7.5 That is, y(t) = C'e²t +7.5.
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