# Differential Equations

> Equations involving derivatives

- Skill: `ffsshhttiikk/differential-equations` (Agent Skill)
- Install (CLI): `npx skillmds@latest add ffsshhttiikk/differential-equations`
- Raw SKILL.md: https://api.skillmd.com/api/skills/ffsshhttiikk/differential-equations/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- License: MIT
- Author: ffsshhttiikk (https://skillmd.com/u/ffsshhttiikk)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/ffsshhttiikk/differential-equations

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## What I do
- Solve first-order ODEs (separable, linear, exact)
- Solve higher-order linear ODEs with constant coefficients
- Apply Laplace transforms for ODE solutions
- Solve systems of differential equations
- Analyze stability of equilibrium solutions
- Solve partial differential equations

## When to use me
When modeling dynamic systems, physics problems, or any system involving rates of change.

## Key Concepts
- **First-Order Linear**: dy/dx + P(x)y = Q(x), integrate factor μ = e^{∫Pdx}
- **Separable**: dy/dx = f(x)g(y), ∫dy/g(y) = ∫f(x)dx
- **Second-Order Linear**: ay'' + by' + cy = 0, characteristic r² + br/a + c/a = 0
- **Laplace Transform**: L{f(t)} = ∫₀^∞ e^{-st}f(t)dt, converts ODEs to algebraic
- **Particular Solution**: Sum of homogeneous + particular solves full equation
- **Phase Lines**: Visualize equilibrium stability for autonomous ODEs