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Agent skill

Second Order Odes

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for second order odes in odes pdes

MITAuto-check: notesResearch & Science

Install Second Order Odes

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill second-order-odes -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 second-order-odes --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .claude/skills && cp -r skills-src/.claude/skills/math/odes-pdes/second-order-odes .claude/skills/second-order-odes && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
second-order-odes
GitHub stars
3.9k
Used in
1 other repo
Token cost
~830 tokens
SKILL.md length
345 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

Problem-solving strategies for second order odes in odes pdes

  • Works in 5 steps: Classify the ODE → Homogeneous with Constant Coefficients → Particular Solution (Non-homogeneous) → …
  • Tasks that involve Math and symbolic computation
  • SKILL.md covers When to Use, Decision Tree, Tool Commands and Key Techniques, plus 1 more section
  • Calls uv

What it does

Second Order Odes is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for second order odes in odes pdes

Its SKILL.md is about 830 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.

It sits in Research & Science, covering Math and symbolic computation. It works with SymPy. The repository describes itself as: Context management for Claude Code. Hooks maintain state via ledgers and handoffs. MCP execution without context pollution. Agent orchestration with isolated context windows. The licence is MIT.

When your agent uses it

  • Tasks that involve Math and symbolic computation

Example prompts

  • “/second-order-odes”

Requirements

  • Python 3
  • Pre-approved tools (allowed-tools): Bash, Read

Workflow steps

5 steps, taken from the first numbered list in SKILL.md.

  1. Classify the ODE
  2. Homogeneous with Constant Coefficients
  3. Particular Solution (Non-homogeneous)
  4. Numerical Solution
  5. Boundary Value Problems

What it can do on your machine

Read from SKILL.md and the folder at commit d07ff4b. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves these tools, so the agent can use them without asking each time:

    • Bash
    • Read

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    Shell commands in SKILL.md call:

    • uv

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md. Its commands use uv, which can reach the network depending on how they are called.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Second Order Odes loads about 830 tokens when it runs. Until then it costs about 20 tokens; SKILL.md has 345 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~20
When it runs · the whole SKILL.md, loaded when a task matches
~830

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check: notes

The automated check noted patterns worth knowing about, such as sudo or a known installer.

  • NotePre-approves every shell command (allowed-tools: Bash)SKILL.md
    allowed-tools: Bash, Read

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

The full file from parcadei/Continuous-Claude-v3 at commit d07ff4b, republished under its MIT licence (© parcadei). 345 words, ~830 tokens.

Download SKILL.mdSave it as .claude/skills/second-order-odes/SKILL.md (or your agent's skills folder).
name
second-order-odes
description
Problem-solving strategies for second order odes in odes pdes
allowed-tools
Bash, Read

Second Order Odes

When to Use

Use this skill when working on second-order-odes problems in odes pdes.

Decision Tree

  1. Classify the ODE

    • Constant coefficients: ay'' + by' + cy = f(x)?
    • Variable coefficients: y'' + P(x)y' + Q(x)y = R(x)?
    • Cauchy-Euler: x^2 y'' + bxy' + cy = 0?

  2. Homogeneous with Constant Coefficients

    • Characteristic equation: ar^2 + br + c = 0
    • Distinct real roots: y = c1e^{r1x} + c2e^{r2x}
    • Repeated root: y = (c1 + c2x)e^{rx}
    • Complex roots a +/- bi: y = e^{ax}(c1cos(bx) + c2sin(bx))
    • sympy_compute.py solve "a*r**2 + b*r + c" --var r

  3. Particular Solution (Non-homogeneous)

    • Undetermined coefficients: guess based on f(x)
    • Variation of parameters: y_p = u1y1 + u2y2
    • sympy_compute.py dsolve "y'' + y = sin(x)"

  4. Numerical Solution

    • Convert to first-order system: let v = y', then v' = y''
    • solve_ivp(system, [t0, tf], [y0, v0])

  5. Boundary Value Problems

    • Shooting method: guess initial slope, iterate
    • scipy.integrate.solve_bvp(ode, bc, x, y_init)

Tool Commands

Scipy_Solve_Ivp_System
bash
uv run python -c "from scipy.integrate import solve_ivp; sol = solve_ivp(lambda t, Y: [Y[1], -Y[0]], [0, 10], [1, 0]); print('y(10) =', sol.y[0][-1])"
Sympy_Charpoly
bash
uv run python -m runtime.harness scripts/sympy_compute.py solve "r**2 + r + 1" --var r
Sympy_Dsolve_2Nd
bash
uv run python -m runtime.harness scripts/sympy_compute.py dsolve "Derivative(y,x,2) + y"

Key Techniques

From indexed textbooks:

  • [An Introduction to Numerical Analysis... (Z-Library)] Modern Numerical Methods for Ordinary Wiley, New York. User's guide for DVERK: A subroutine for solving non-stiff ODEs. Keller (1966), Analysis of Numerical Methods.
  • [Elementary Differential Equations and... (Z-Library)] Riccati equation and that y1(t) = 1 is one solution. Use the transformation suggested in Problem 33, and nd the linear equation satised by v(t). Find v(t) in the case that x(t) = at, where a is a constant.
  • [An Introduction to Numerical Analysis... (Z-Library)] Test results on initial value methods for non-stiff ordinary differential equations, SIAM J. Comparing numerical methods for Fehlberg, E. Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnumg mit Schrittweiten-Kontrolle und ihre Anwendung auf Warme leitungsprobleme, Computing 6, 61-71.
  • [Elementary Differential Equations and... (Z-Library)] Two papers by Robert May cited in the text are R. May,“Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos,” Science 186 (1974), pp. Biological Populations Obeying Difference Equations: Stable Points, Stable Cycles, and Chaos,” Journal of Theoretical Biology 51 (1975), pp.
  • [An Introduction to Numerical Analysis... (Z-Library)] COLSYS: collocation software for boundary-value ODEs, ACM Trans. Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations. Elementary Differential Equations and Boundary Value Problems, 4th ed.

Cognitive Tools Reference

See .claude/skills/math-mode/SKILL.md for full tool documentation.

© parcadei, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

Just SKILL.md in .claude/skills/math/odes-pdes/second-order-odes of parcadei/Continuous-Claude-v3.

Open the folder on GitHubat commit d07ff4b

Used in 1 other repository

We found 1 copy of this SKILL.md (exact, near-identical or edited) in other folders, from 1 other GitHub owner. This page covers the copy in parcadei/Continuous-Claude-v3, which our catalogue first saw on October 7, 2026.

Compare with similar skills

Second Order Odes next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.

Second Order Odes compared with similar skills
SkillStarsUsed inTokensAuto-checkLicenceRepo updated
Second Order Odes this skillparcadei/Continuous-Claude-v33.9k1 repos~830Automated safety check: NotesMIT
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Edu Solid Geometrywy51ai/edulab1.4k1 repos~1.1kAutomated safety check: PassApache-2.0
Math Toolsananddtyagi/cc-marketplace6872 repos~1.3kAutomated safety check: PassNone
Edu Chem Reactionwy51ai/edulab1.4k—~1.2kAutomated safety check: PassApache-2.0

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Works with

Categories

Questions about Second Order Odes

What does Second Order Odes do?

Problem-solving strategies for second order odes in odes pdes. Second Order Odes is an agent skill from parcadei/Continuous-Claude-v3.

When should I use Second Order Odes?

Second Order Odes fits situations like: tasks that involve Math and symbolic computation.

How do I install Second Order Odes in Claude Code?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill second-order-odes -a claude-code`. Or copy the skill folder (.claude/skills/math/odes-pdes/second-order-odes in parcadei/Continuous-Claude-v3) into .claude/skills/second-order-odes in your project. Claude Code loads it when a task matches its description.

How do I install Second Order Odes in Codex?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill second-order-odes -a codex`. Or copy the skill folder (.claude/skills/math/odes-pdes/second-order-odes in parcadei/Continuous-Claude-v3) into .agents/skills/second-order-odes in your project. Codex loads it when a task matches its description.

Can I use Second Order Odes in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add parcadei/Continuous-Claude-v3 --skill second-order-odes -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/second-order-odes, .gemini/skills/second-order-odes, .github/skills/second-order-odes and .opencode/skills/second-order-odes in your project.

What does Second Order Odes need to run?

Going by SKILL.md and its folder, Second Order Odes needs the command-line tools its instructions call (uv). Our summary lists: Python 3. Its frontmatter pre-approves these tools: Bash, Read.

Does Second Order Odes access the network?

SKILL.md contains no URLs. Its commands use uv, which can reach the network depending on how they are called. This is read from the text; nothing was executed.

Is Second Order Odes safe to install?

Our automated static check of SKILL.md found notes only (pre-approves every shell command (allowed-tools: bash)), nothing it rates as a warning. It is not a guarantee. Review the folder before installing.

What licence does Second Order Odes use?

Second Order Odes is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.

How many tokens does Second Order Odes use?

About 830 tokens (SKILL.md is roughly 3.3k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.

What are the alternatives to Second Order Odes?

Skills that share tags, products or a category with Second Order Odes: Sympy (zLanqing/codex-claude-academic-skills, 4.6k stars), Edu Analytic Geometry (wy51ai/edulab, 1.4k stars), Edu Solid Geometry (wy51ai/edulab, 1.4k stars) and Math Tools (ananddtyagi/cc-marketplace, 687 stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Second Order Odes?

parcadei (a GitHub user) maintains it in parcadei/Continuous-Claude-v3, which has 3,940 GitHub stars. The repository holds 141 skills in this directory. The repository was last updated on January 26, 2026.

Source: parcadei/Continuous-Claude-v3 on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.