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python - time evolution of a matrix?

I want to compute the time-evolution of the matrix :U = exp(-iHt) for a given time Then I want to multiply this matrix U by the matrix X in order to obtain the evolution of this matrix. I have found the following library in python for evolution vector v:

exact = scipy.integrate.ode(-(1j)*T*Hint,rho0)
print (exact)

This code is for time evolution of a vector . How to evaluat the density matrix using this code? I know mesolve command in qutip package but I have another solution for calculate time evolution of the matrix X

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