Installation

pip install -r requirements.txt streamlit run app.py

ode_solver

Interactive Laplace-based solver for second-order linear ODEs with visualization.

Second-Order Linear ODE Solver (Symbolic + Visualization)

An interactive Streamlit application for solving second-order linear ODEs with constant coefficients using:

• Symbolic Laplace transforms
• Symbolic convolution (Green's function)
• Exact handling of real, repeated, and complex roots
• Phase plane visualization
• Arbitrary forcing functions (including Heaviside)

Features

• Solves: y'' + b y' + c y = x(t)
• Exact symbolic solution with applied initial conditions
• Time-domain plot of y(t)
• Phase plane plot (y vs y')
• Automatic handling of complex conjugate roots
• Matches Wolfram Alpha on standard test cases

Example

$$y'' + 2y' + 5y = \sin(t), \quad y(0)=1, \; y'(0)=0$$