How to use dynamic programming for finding all possible paths from source to destination?

I am trying to find all possible paths from a given source to destination. I created a directed acyclic graph using the NetworkX library of python. Finding all possible paths is a time exponential problem. I have seen a lot of suggestions about using dynamic programming to improve timing but I could not find any solution that how can I use dynamic programming in this case. Here are the three different approaches I am using for finding all possible paths between two nodes. First approach,

def find_all_paths(graph, start, end, path=[]):
path = path + [start]
if start == end:
    return [path]
paths = []
for node in graph[start]:
    if node not in path:
        newpaths = find_all_paths(graph, node, end, path)
        for newpath in newpaths:
            paths.append(newpath)
return paths

Second approach,

def all_simple_paths(G, source, target, cutoff=None):
if source not in G:
 raise nx.NetworkXError('source node %s not in graph'%source)
if target not in G:
 raise nx.NetworkXError('target node %s not in graph'%target)
if cutoff is None:
cutoff = len(G)-1
if G.is_multigraph():
 raise NetworkXError("astar_path() not implemented for Multi(Di)Graphs")
 else:
  return _all_simple_paths_graph(G, source, target, cutoff=cutoff)


def _all_simple_paths_graph(G, source, target, cutoff=None):
if cutoff < 1:
return
visited = [source]
stack = [iter(G[source])]
while stack:
children = stack[-1]
child = next(children, None)
if child is None:
    stack.pop()
    visited.pop()
elif len(visited) < cutoff:
    if child == target:
        yield visited + [target]
    elif child not in visited:
        visited.append(child)
        stack.append(iter(G[child]))
else: #len(visited) == cutoff:
    if child == target or target in children:
        yield visited + [target]
    stack.pop()
    visited.pop()

Third approach,

def printAllPathsUtil(G, u, d, visited, path): 

sid = G.node[u]['nodeID']
did = G.node[d]['nodeID']

# Mark the current node as visited and store in path 
visited[sid]= True
path.append(u) 

# If current vertex is same as destination, then print 
# current path[] 
if u == d: 
global pathlist
pathlist.append(path) 
else: 
# If current vertex is not destination 
#Recur for all the vertices adjacent to this vertex 
for i in G.neighbors(u):
    j =  G.node[i]['nodeID']
    if visited[j]==False: 
        printAllPathsUtil(G, i, d, visited, path) 

# Remove current vertex from path[] and mark it as unvisited 
path.pop() 
visited[sid]= False

def printAllPaths(G,s, d):
# Mark all the vertices as not visited 
visited =[False]*G.number_of_nodes() 

# Create an array to store paths 
path = [] 
global pathlist
# Call the recursive helper function to print all paths 
printAllPathsUtil(G, s, d,visited, path)

return pathlist

Any help in this regard is appreciated.

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