Differential Equation Analyzer

A web application for analyzing, solving, and visualizing differential equations. This application provides tools for checking linearity, verifying solutions, and visualizing differential equations.

Features

• Linearity Checker: Determine if a differential equation is linear or non-linear
• Solution Verifier: Check if a function is a solution to a given differential equation
• Visualization: Plot solutions to differential equations
• API Endpoints: Access the functionality programmatically

Local Development Setup

Prerequisites

• Python 3.9
• pip (Python package manager)
• Virtual environment (recommended)

Installation

1. Clone the repository:

   git clone <repository-url>
   cd differential-equation-app
   

2. Create and activate a virtual environment:

   python -m venv venv
   source venv/bin/activate  # On Windows: venv\Scripts\activate
   

3. Install dependencies:

   pip install -r requirements.txt
   

4. Run the application:

   ./run_app_simple.sh
   

   Or directly with Python:

   python app.py
   

5. Access the application at: http://127.0.0.1:5001

Docker Deployment

Prerequisites

• Docker
• Docker Compose

Running with Docker

1. Build and start the container:

   ./docker-run.sh
   

   Or manually:

   docker-compose build
   docker-compose up -d
   

2. Access the application at: http://localhost:5001

3. View logs:

   docker-compose logs -f
   

4. Stop the container:

   docker-compose down
   

Deployment Options

Netlify

The application is configured for deployment on Netlify using the following files:

• netlify.toml: Configuration for build settings and redirects
• netlify-build.sh: Custom build script for Netlify

Vercel

The application is configured for deployment on Vercel using the following files:

• vercel.json: Configuration for build settings and environment variables
• vercel-build.sh: Custom build script for Vercel
• .vercel/project.json: Project configuration for Vercel

Example Equations to Try

• Linear first-order equation: y' + 2*y = sin(x)
• Non-linear equation: y' = y^2 * sin(x)
• Second-order linear equation: y'' + 4*y = 0

API Usage

The application provides API endpoints for programmatic access:

• /api/check_linearity: Check if an equation is linear
• /api/verify_solution: Verify if a function is a solution to an equation
• /api/visualize: Generate visualization data for an equation

Example API request:

curl -X POST http://localhost:5001/api/check_linearity \
  -H "Content-Type: application/json" \
  -d '{"equation": "y\' + 2*y = sin(x)"}'

License

MIT License