These are review problems i need help with. Dont know if i getting the right ans

Question

These are review problems i need help with. Dont know if i getting the right answer.

The system x'(t) = Ax has four linearly independent eigenvectors associated with its eigenvalues -1 and 1 Let B be the reduced row echelon form of the matrix (A - I). Find two linearly independent eigenvectors associated with the eigenvalue 1 given B below. Find the solution of the initial value problem x(0) = , x'(t) = x. Sketch a phase portrait for the system including the trajectory through the given initial point. Have arrows indicate the behavior of the trajectory as t increases. Find the general solution of the system x'(t) = x. Find the general solution of the system x'(t) = x. Transform the equation ty"' - (t2)y'/ + (sint)y = et into an equivalent first order system. Given the first order system x'(t) = x, find the critical values of alpha where the qualitative nature of the phase portrait for the system changes, describe the nature of the phase portrait/classification of the origin and give the intervals of values of alpha that correspond to that type of phase portrait.

Explanation / Answer

5)

Take y = x1 , y' = x2 and y" = x3

We have:

x1' = x2

x2' = x3

x3' = y"' = (t^2 y' - sin(t)y +e^t)/t = t*x2 - (sin(t)/t)x1 + e^t/t

So we can write the system:

X' = AX + B

where:

A =

[0       1     0

0       0      1

-sint/t   t    0 ]

and

B =

[0

0

e^t/t]

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.