# Matrix ODE

by Manchot
Tags: matrix
 P: 728 I'm trying to find a general solution for the logistic ODE $\frac{dU}{dx}=A(I-U)U$, where A and U are square matrices and x is a scalar parameter. Inspired by the scalar equivalent I guessed that $U=(I+e^{-Ax})^{-1}$ is a valid solution; however, $U=(I+e^{-Ax+B})^{-1}$ is not when U and A don't commute. Any ideas?