The system of first order differential equations y₁ = −4y₁ + 5y2 +1 y2 = 5y₁ - 4y2 +1 where y₁ (0) = 0, y₂ (0) = 0 has solution y₁(t)= 3 t 10/20 5 + 5 -9t t 2 -9t e y2(t) = ²/3e² + 2²/1² 5 - 1 1 5

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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The system of first order differential equations
y₁ = −4y₁ + 5y2 +1
y2 = 5y₁ - 4y2 +1
where y₁ (0) = 0, y₂ (0) = 0
has solution
y₁(t)=
3 t
10/20
5
+
5
-9t
y2(t) = ¹ + 2²/1²
3 t 2 -9t
e
e
5
- 1
1
5
Transcribed Image Text:The system of first order differential equations y₁ = −4y₁ + 5y2 +1 y2 = 5y₁ - 4y2 +1 where y₁ (0) = 0, y₂ (0) = 0 has solution y₁(t)= 3 t 10/20 5 + 5 -9t y2(t) = ¹ + 2²/1² 3 t 2 -9t e e 5 - 1 1 5
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