DSolve[{Derivative[1][x][t] == 6*x[t] - 72*y[t] + 44*z[t], Derivative[1][y][t] == 4*x[t] - 4*y[t] + 26*z[t], Derivative[1][z][t] == 6*x[t] - 63*y[t] + 38*z[t]},{x[t], y[t], z[t]},t]