- #1
Manchot
- 473
- 4
I'm trying to find a general solution for the logistic ODE [itex]\frac{dU}{dx}=A(I-U)U[/itex], where A and U are square matrices and x is a scalar parameter. Inspired by the scalar equivalent I guessed that [itex]U=(I+e^{-Ax})^{-1}[/itex] is a valid solution; however, [itex]U=(I+e^{-Ax+B})^{-1}[/itex] is not when U and A don't commute. Any ideas?