How can we solve $M^t (dM/dx) = C$?

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We have $M[x]$ and $C$ as $3 \times 3$ matrices. If $M^t (dM/dx) = C$, and $C$ is a constant skew-symmetric matrix. How can we solve for $M$?

Boundary conditions: $M =$ Identity matrix at $x$ =0.

You may suggest a way to solve it in Mathematica.