dx dt +2X + dy dt. +6y= 2²- 2 dx + 3x + 3 dy dt dE +8y=1
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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Question
Transcribed Image Text:5
Solve the following Systems of ODES %
dx
dy +6y=2 € ²
dt.
●
dt
+2X +
2dx + 3x + 3 dy +8y=
dt
dE
-t
(D+5) X + (D+4)y=e
(D+2)X + (D+1)=y=3
}A
Ansa
• (2D+3)X + (D+4)y = - cost
(D+1) X + (D+2)y = 2 sint.
Anss
zt t
X (t) = 4₁ e ² + (₂²+5² +!
at t
-t
y(t) = k₁e +k₂²e-11e²-3
X(t) = 4
y(t) = -5 + 1² e ²
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