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Forums
Mathematics
Differential Equations
Non-homogeneous systems with repeated eigenvalues
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[QUOTE="wrobel, post: 5467885, member: 593228"] Sure you can. Actually this question is not about eigenvalues 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## [/QUOTE]
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Forums
Mathematics
Differential Equations
Non-homogeneous systems with repeated eigenvalues
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