🧮 Differential Equation Solver – GUI Application

An interactive full-screen Python tool for solving nth-order linear ODEs with constant coefficients, now with new features in update.py.

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📌 Project Structure

ddifferential-equation-solver/
│
├── LICENSE # Project license
├── README.md # Project documentation
├── main.py # Original stable version (renamed from DiffEqn Solver.py)
├── update.py # New features and enhancements
│
└── figures/ # Folder for images and outputs
├── general_GUI.png # Screenshot of GUI
├── sample_output.png # Original sample output
└── updated_sample_output.png # Updated sample output

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⚙️ main.py — Original Features

The base version supports:

• ✅ Solves nth-order linear ODEs with constant coefficients (up to 6th order)
• ✅ Auto-computes:
  • Auxiliary (characteristic) equation
  • Roots (real, complex, repeated)
  • Complementary function (CF)
• ✅ Displays time taken for computation
• ✅ Live equation preview while typing coefficients
• ✅ Real-world applications shown for each equation order
• 🖥️ Full-screen GUI with tkinter
• 🧠 Symbolic computation via sympy

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✨ update.py — New & Improved Features

• 🔹 Enhanced Input System
  • Better coefficient handling with error validation
  • Support for quick clearing and resetting input fields
• 🔹 Step-by-Step Solution Mode
  • Shows derivation of CF with explanations
  • Highlights root multiplicity in detail
• 🔹 Extended Output
  • Adds equation order classification (overdamped, oscillatory, etc.)
  • Displays root plots for visual understanding
• 🔹 UI Improvements
  • Cleaner font styles and dynamic resizing
  • Option to toggle dark/light mode
• 🔹 Performance Boost
  • Optimized symbolic computations for large-order equations

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📷 Screenshots

Full Old GUI View

Full New GUI View

Sample Output

• Old version (main.py) View full image

• New version (update.py) View full image

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🧰 Technologies & Concepts

Domain	Tools / Concepts Used
Programming Language	Python 3
GUI Toolkit	tkinter
Symbolic Computation	sympy (including dsolve, sympify)
Math Foundation	Linear ODEs, Method of Undetermined Coefficients, Cauchy-Euler Equations, CF, PI, GS
Development Practice	Modular design, Event-driven programming, Dynamic UI generation, Error handling

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▶️ Getting Started

✅ Prerequisites

• Python 3.8 or higher
• A virtual environment (e.g., venv or conda) is highly recommended.

🔧 Installation

1. Clone this repository:

   git clone [https://github.com/Sanjaykumar030/DiffEqnSolver.git](https://github.com/Sanjaykumar030/DiffEqnSolver.git)
   cd DiffEqnSolver

2. Install dependencies:

   pip install -r requirements.txt

3. Run the application:

   python update.py

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🧠 Educational Value

The update.py version transforms this tool into a comprehensive learning environment. It reinforces:

• The structural differences between Homogeneous, Non-Homogeneous, and Cauchy-Euler equations.
• The concept of the complete solution ($y = y_c + y_p$).
• How the form of $f(x)$ influences the Particular Integral.
• The application of advanced solving techniques in a transparent, visual manner.

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⚠️ Limitations (in update.py)

• The non-homogeneous solver's effectiveness depends on sympy's ability to solve for the PI, which is powerful but may not cover every esoteric function.
• Currently does not solve systems of ODEs or equations with variable coefficients beyond the Cauchy-Euler form.
• Non-linear equations are not supported.

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📜 License

This project is licensed under the MIT License. See the LICENSE file for usage rights and permissions.

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🙋 Author

Sanjay Kumar Sakamuri Kamalakar

• 📧 Email: sksanjaykumar010307@gmail.com
• 🔗 LinkedIn: linkedin.com/in/sanjay-kumar-sakamuri-kamalakar-a67148214
• 🧪 ORCID: 0009-0009-1021-2297

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🙏 Acknowledgements

• OpenAI’s ChatGPT for architectural and code logic support in the update.py refactor.
• The developers and communities behind Python, tkinter, and sympy.