differential-equations
Equations involving derivatives
Source facts
- Repository
- ffsshhttiikk/opencode-agents-skills
- Last source activity
- February 28, 2026 at 22:49
- Detected SKILL.md language
- English
- Stars
- 3
- Forks
- 2
Install options
The review-first prompt is selected by default. You can switch to a direct command or download a local copy.
Review the source files
Read SKILL.md and any companion files shown by SkillsMP before deciding whether to install.
Showing SKILL.md
SKILL.md
Source instructions · Read-only preview- name
- differential-equations
- description
- Equations involving derivatives
- license
- MIT
- compatibility
- opencode
- metadata
- {"audience":"mathematicians","category":"mathematics"}
## 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
View on GitHub