Find the solution of the given initial value problem. y" + 2y' + 2y = cost + 8(1 - 5); y(0) = 5, y' (0) = 4 y) = - taz()ef"cost + cos( Se" +) + sine (9e + + sint( 9e- + 24 Un/2(1)e sint + sint 42 + cost 5° y(t) = + 5 x) = - ta)et"cost + cos(+) + sine ( +) 24 - Uz/2(t)ez¯'cost + cost( 5 42 5 24 42 y(t) = Un/2(1)e¯† cost + cost + sint 5 re -e + 5 5 24 y(t) = un/2(t)e'sint + cost 5 + 5 42 + sint 5 + 5
Find the solution of the given initial value problem. y" + 2y' + 2y = cost + 8(1 - 5); y(0) = 5, y' (0) = 4 y) = - taz()ef"cost + cos( Se" +) + sine (9e + + sint( 9e- + 24 Un/2(1)e sint + sint 42 + cost 5° y(t) = + 5 x) = - ta)et"cost + cos(+) + sine ( +) 24 - Uz/2(t)ez¯'cost + cost( 5 42 5 24 42 y(t) = Un/2(1)e¯† cost + cost + sint 5 re -e + 5 5 24 y(t) = un/2(t)e'sint + cost 5 + 5 42 + sint 5 + 5
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:Find the solution of the given initial value problem.
y" + 2y' + 2y = cost +
8(1 - 5); y(0) = 5, y' (0) = 4
y) = - taz()ef"cost + cos( Se" +) + sine (9e +
+ sint( 9e- +
24
Un/2(1)e sint + sint
42
+ cost
5°
y(t) =
+
5
x) = - ta)et"cost + cos(+) + sine ( +)
24
- Uz/2(t)ez¯'cost + cost(
5
42
5
24
42
y(t) = Un/2(1)e¯† cost + cost
+ sint
5
re
-e
+
5
5
24
y(t) = un/2(t)e'sint + cost
5
+
5
42
+ sint
5
+
5
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