• Support PF! Buy your school textbooks, materials and every day products Here!

Ordinary Differential Equation System with Variable Coefficients

  • #1

Homework Statement


For [tex]t\in\mathbb{R}[/tex], let:

[tex]A=\left[\begin{array}{ccc}
-1 & 0 & 0\\
0 & 2 & 2t\\
0 & 0 & 2\end{array}\right][/tex]

Get the solution for the general equation: [tex] X'=A(t)X [/tex]

Homework Equations



The Attempt at a Solution


I done many of these problems, all with constant coefficients, but I don't know how to do in this case.
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
Did you know that the solution to
[tex]x'(t) = f(t) x(t)[/tex]
is
[tex]x(t) = x_0 \exp\left( \int_{t_0}^t f(\xi) \, d\xi \right)[/tex]
?
 
  • #3
Yes, I know. That's the formula I use after getting the exponential matrix, by "diagonalizing" the matrix A. My problem is that I'm not sure if I can do it as I do with constant coefficients, because supposedly it should be different.
 

Related Threads for: Ordinary Differential Equation System with Variable Coefficients

Replies
22
Views
4K
Replies
6
Views
859
Replies
13
Views
2K
Replies
6
Views
2K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
997
  • Last Post
Replies
2
Views
729
Top