Implement the function that searches a given value x in linked list headed with node nil.

Sure, here's an implementation of the function in Python:

class Node:
    def __init__(self, value):
        self.value = value
        self.next = None

def search_linked_list(nil, x):
    node = nil.next
    while node is not None:
        if node.value == x:
            return node
        node = node.next
    return None

Here, `nil` is the head of the linked list, which is typically a dummy node with no value that serves as a placeholder. The `search_linked_list` function takes in `nil` and the value `x` to search for, and returns the node in the linked list that contains `x`, or `None` if `x` is not found.

The function works by starting at the first node after `nil`, and iterating through the linked list until it finds the node with the value `x`. If it traverses the entire linked list without finding `x`, it returns `None`.

Note that this implementation assumes that the values in the linked list are unique. If there can be multiple nodes with the same value, you may need to modify the function to return a list of nodes instead of just one.