Systems of Differential Equations

Bryon0101 · **Joined:** Mon, 5 Dec 2011 18:50:51 UTC **Posts:** 2

Hi

I have a question about how to start solving systems of equations.

The question asks to solve an IVP of X' = [2 4]X; (2 x 2 matrix) X(0) = [1] (1 x 2 matrix)
. ..............................................[3 -2]............................[0]

Is this a problem akin to the eigenvector, where X = [x1]?
. ........................................................... [x2]

Thanks!

outermeasure · **Posted:** Tue, 6 Dec 2011 11:00:10 UTC

Bryon0101 wrote:

Hi

I have a question about how to start solving systems of equations.

The question asks to solve an IVP of X' = [2 4]X; (2 x 2 matrix) X(0) = [1] (1 x 2 matrix)
. ..............................................[3 -2]............................[0]

Is this a problem akin to the eigenvector, where X = [x1]?
. ........................................................... [x2]

Thanks!

Depends on what you mean by akin. You could have just written down $X=\exp(\begin{pmatrix}2&4\\3&-2\end{pmatrix}t)X(0)$ without ever thinking about eigenvectors and eigenvalues.

S.O.S. Mathematics CyberBoard

Systems of Differential Equations

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