first-order-odes

You can solve a first-order ODE symbolically by using SymPy to classify the equation and apply analytical methods like integrating factors or separation of variables. This skill automates that classification and solution process.

For numerically integrating an initial value problem, this skill leverages SciPy's `solve_ivp` function. It computes approximate numerical solutions for first-order ODEs when analytical methods are insufficient or unavailable.

Classifying a differential equation involves checking its structural form against known patterns. This skill analyzes the ODE structure to identify whether it is linear, separable, exact, or Bernoulli, which determines the valid solution method.

Yes, you need both SciPy and SymPy installed in your Python environment. SciPy handles numerical integration for initial value problems, while SymPy provides the symbolic math capabilities required for analytical solutions.

To analyze equilibria in autonomous ODEs, this skill finds equilibrium points and generates phase portrait visualizations. This helps understand the long-term qualitative behavior and stability of the dynamical system.