Given the following linear system of ODE: V₁' = 4V₁ +2V₂ V2' = 10/1-4/2 Solve the initial value problem, given y₁ (0) = 1 and y₂(0) = 2 O 1 e-6t y = 7/6 [1] e [1]et - 1/6 [¹] - [1] y = et + [2] =-1[1] y = + 5/6 [ -= ²¹] e- [3] ebt + -1/0+5/01/ y= y = -6t e e³t+ e-3t e-6t h e-bt
Given the following linear system of ODE: V₁' = 4V₁ +2V₂ V2' = 10/1-4/2 Solve the initial value problem, given y₁ (0) = 1 and y₂(0) = 2 O 1 e-6t y = 7/6 [1] e [1]et - 1/6 [¹] - [1] y = et + [2] =-1[1] y = + 5/6 [ -= ²¹] e- [3] ebt + -1/0+5/01/ y= y = -6t e e³t+ e-3t e-6t h e-bt
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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![Given the following linear system of ODE:
V₁' = 4V1 +2V2
V₂' = 10/₁-4/2
Solve the initial value problem, given y₁ (0) = 1 and y₂ (0) = 2
O
y = 7/6
O
y =
et +
O --8--8-
H
y
[1]
H
y=-1
ebt
= [2] e e³t+5/6
-¹ [He
y = 1/6
L
- 1/6 [15]
ebt
+
23
-6t
5
e-6t
e-3t
e-ot
1/6[1]eºt +5/6 [11/5] 0
e
h
-6t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9bdea08a-40de-450d-a706-ffb194141953%2Fd6b32bed-b15f-4182-9a10-3e904be46148%2Fngo256w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the following linear system of ODE:
V₁' = 4V1 +2V2
V₂' = 10/₁-4/2
Solve the initial value problem, given y₁ (0) = 1 and y₂ (0) = 2
O
y = 7/6
O
y =
et +
O --8--8-
H
y
[1]
H
y=-1
ebt
= [2] e e³t+5/6
-¹ [He
y = 1/6
L
- 1/6 [15]
ebt
+
23
-6t
5
e-6t
e-3t
e-ot
1/6[1]eºt +5/6 [11/5] 0
e
h
-6t
![f(x)= |x| (-2<x<2), p = 4
for the given periodic function, what is the Fourier series of f?
O
an=
bn=0
8
n²π²
an=
bn=0
o an
an =
bn=0
bn
4
n²π²
=
an=
bn=0
-COS (NTT)
4
2
n²π²
-[(-1)" - 1]
-cos (nπ)
4
n²π7²
-sin(nπ)
4
2
n²π²
4
2 2
nπ
-cos (nπ)
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9bdea08a-40de-450d-a706-ffb194141953%2Fd6b32bed-b15f-4182-9a10-3e904be46148%2Fu3p2zi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:f(x)= |x| (-2<x<2), p = 4
for the given periodic function, what is the Fourier series of f?
O
an=
bn=0
8
n²π²
an=
bn=0
o an
an =
bn=0
bn
4
n²π²
=
an=
bn=0
-COS (NTT)
4
2
n²π²
-[(-1)" - 1]
-cos (nπ)
4
n²π7²
-sin(nπ)
4
2
n²π²
4
2 2
nπ
-cos (nπ)
4
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