[math]\frac{\text{d}x}{\text{d}t}=Ax , {\text{d}x} x^{-1}=A {\text{d}t} [/math] , [math]{\text{now taking transpose on both sides}}[/math] [math] \int_{C}^{x} x^{-T}{\text{d}x^{T}}=\int_{0}^{t}A {\text{d}t} {\text{ solution becomes }} {\text x =(e^{t^{T}A^{T}})^{T} C}, {\text {but actual answer } x = (e^{At}) C, how?} [/math]
insincere question