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But then the answer is fine, since for each of the 9 matrix elements either A1 or Dmf has a zero entry, which results in a product of 0.
Multiplying both the left and right side of the first two equations by r^2 clears r from the denominator. Then DSolve can solve the system. (I edited ths since first posted -- I didn't notice the independent variable in the earlier assignment to t1...