2026-04-04 15:19:50.1775315990
How to prove the Abel's Theorem for linear ODE equations system? (see the picture)
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It is because $\newcommand{\eps}{\varepsilon}\newcommand{\tr}{\operatorname{tr}}$ $$ \det(A+\eps B)=\det(A)\det(I+\eps A^{-1}B)=\det(A)(1+\eps \tr(A^{-1}B)+O(\eps^2)) $$ The derivative of the determinant follows, then insert the ODE.