The coefficient matrix for a system of linear differential equations of the form y^1=Ay

Burhan Hopper 2021-01-04 Answered

The coefficient matrix for a system of linear differential equations of the form y1=Ay  has the given eigenvalues and eigenspace bases. Find the general solution for the system 

λ1=3[110]

λ2=0[151][214]

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Expert Answer

Bella
Answered 2021-01-05 Author has 81 answers
By theorem 6.19 we know that the solution is
y=c1eλ1tu1++cneλntun
with λi the eigenvalues of the matrix A nad u_i the eigenvectors Thus for this case we then obtain the general solution:
[y1y2y3]=y=c1e3t[110]+c2e0t[151]+c3e0t[214]
Thus we obtain:
y1=c1e3t+c2e0t+2c3e0t=c1e3t+c2+2c3
y2=c1e3t+5c2e0t+c3e0t=c1e3t+5c2+c3
y3=c2e0t+4c3e0t=c2+4c3
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