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.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 33CR
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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
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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