(a) Find a fundamental matrix for the given system of

siroticuvj

siroticuvj

Answered question

2021-11-23

(a) Find a fundamental matrix for the given system of equations.(b) Also find the fundamental matrix Φ(t)satisfying Φ(0)=I

Answer & Explanation

Lupe Kirkland

Lupe Kirkland

Beginner2021-11-24Added 21 answers

The eigenvalues and related eigenvectors must first be determined. Next, determine a broad answer to the d.e. Create a basic matrix next. After that, solve the constants c1,c2,c3,c4 for the two conditions following from
Φ(0)=[1001]
x=[1411]
(1λ)2+4=0λ2+2λ+5=0λ=1±2i
v1=[2i1]
v2=[2i1]
x=[x1x2]c=et[2sin(2t)2cos(2t)cos(2t)sin(2t)]c
Φ(0)=[1001]
Φ(0)=[1001]
c1=0
2c2=1
c3=1
c4=0
Φ(t)=et[cos(2t)2sin(2t)12sin(2t)cos(2t)]

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