- #1

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Thanks!

- I
- Thread starter faradayscat
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- #1

- 57

- 8

Thanks!

- #2

wrobel

Science Advisor

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Sure you can. Actually this question is not about eigenvaluesQuick question, can you solve non-homogeneous systems with repeated eigenvalues the same ways?

Consider a system ##\dot x=A(t)x+b(t),\quad x\in\mathbb{R}^m##, here ##A(t)## is a square matrix with coefficients depending on t.

The fundamental matrix ##X(t)## is defined by means of the Cauchy problem ##\dot X(t)=A(t)X,\quad X(0)=I##. Then the solution ##x(t),\quad x(0)=\hat x## to the initial inhomogeneous system is given by the formula

##x(t)=X(t)\hat x+\int_0^t X(t)X^{-1}(s)b(s)ds##

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