The general solution to the differential equation y" + y = 0, t > 0 is given by y(t) = C₁ + 7/7. Find the general solution to y" + ¼y = eª.
The general solution to the differential equation y" + y = 0, t > 0 is given by y(t) = C₁ + 7/7. Find the general solution to y" + ¼y = eª.
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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Transcribed Image Text:The general solution to the differential equation y" + y = 0, t > 0
is given by y(t) = C₁ + 7/7.
Find the general solution to y" + y = e.
• y(t) = a₁ + ² + [f²¹e¹ dt = [t
y(t)
= c₁ + ²% + f te ² dt − ²1 [ ² e
t
O y(t) = C₁ +/+czet
te dt
y(t) = C₁ +
t² et dt
1
¹ + ² + √ [ ²³ e²¹ d t = ² / ſ t
dt
te dt
²
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