Here's the `posts.py` file with Pydantic schemas for posts, which can be placed in the `app/api/v1/schemas/` directory:

from typing import Optional
from pydantic import BaseModel
from datetime import datetime

class PostCreate(BaseModel):
    title: str
    content: str

class PostRead(BaseModel):
    id: int
    title: str
    content: str
    created_at: datetime
    updated_at: Optional[datetime] = None

    class Config:
        orm_mode = True

class PostUpdate(BaseModel):
    title: Optional[str] = None
    content: Optional[str] = None

Explanation:

1. `PostCreate` is a Pydantic model that defines the required fields (`title` and `content`) for creating a new post.
3. `PostUpdate` is a Pydantic model that defines the optional fields (`title` and `content`) for updating an existing post.


Note: Make sure to import the necessary dependencies (`typing`, `pydantic`, and `datetime`) at the top of the file.