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First Order Odes · vibeeval | DecimalAI

scienceby vibeeval

First Order Odes

vibeeval/first-order-odes

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for first order odes in odes pdes

NewMaintained

Automatic

Coding pack

Last verified 8/3/2026

What it changes

Passed 8 of 21 test cases with the skill, and 13 of 21 without it.

Without skill60%

With skill40%

Checks it passed that the model alone missed

excludes check_solution
excludes integrating_factor

2 fixed5 passed either way12 still failing3 broke

Pass-rate lift: -20 pp
Tokens: +26%
Agent turns: 0%
Response time: -30%

Model gemini-3.6-flashMeasured 8/3/2026v17 of 22 cases passed with skill · 21 comparable

Tokens, turns and time describe resource use, not a dollar price.

Use this skill

Save it into your project's skills folder. Claude Code picks it up in its next session.

curl -fsSL --create-dirs -o .claude/skills/vibeeval-first-order-odes/SKILL.md https://app.decimal.ai/s/vibeeval-first-order-odes/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-first-order-odes, and start Claude Code with claude --plugin-dir "$(git rev-parse --show-toplevel)/.agents"

1 · One-time — install the CLI (docs ↗)

pip install "decimalai>=0.15"

2 · Get the skill — writes .agents/skills/vibeeval-first-order-odes/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-first-order-odes

No CLI? Get the same file — curl · raw file

curl -fsSL --create-dirs -o .claude/skills/vibeeval-first-order-odes/SKILL.md https://app.decimal.ai/s/vibeeval-first-order-odes/SKILL.md

Raw file: /s/vibeeval-first-order-odes/SKILL.md ↗ · machine-readable summary at /s/vibeeval-first-order-odes.json ↗

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

One of 2 test cases the skill fixed. Same model, same prompt, with and without the skill.

1 of 2

Prompt

I just found an analytical expression for the state variable over time using the symbolic mathematics library. What specific function should I call on the original equation object to verify that the solution satisfies it? Is it 'check_solution'?

What was checked, without and with the skill
Checked	Without skill	With skill
excludes check_solution	Missed	Passed
mentions checkodesol	Passed	Passed

case-10 · gemini-3.6-flash · 8/3/2026 · answers are capped and redacted

What's inside

The instructions your model reads when the skill loads.

SKILL.md69 linessingle file

First Order Odes

When to Use

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

Decision Tree

Classify the ODE
- Linear: y' + P(x)y = Q(x)?
- Separable: y' = f(x)g(y)?
- Exact: M(x,y)dx + N(x,y)dy = 0 with dM/dy = dN/dx?
- Bernoulli: y' + P(x)y = Q(x)y^n?
Select Solution Method

Type Method
Separable Separate and integrate
Linear Integrating factor e^{int P dx}
Exact Find potential function
Bernoulli Substitute v = y^{1-n}
Numerical Solution (IVP)
- scipy.integrate.solve_ivp(f, [t0, tf], y0, method='RK45')
- For stiff systems: method='Radau' or method='BDF'
- Adaptive step size: specify rtol/atol, not step size
Verify Solution
- Substitute back into ODE
- Check initial/boundary conditions
- sympy_compute.py dsolve "y' + y = x" --ics "{y(0): 1}"
Phase Portrait (Autonomous)
- Find equilibria: f(y*) = 0
- Analyze stability: sign of f'(y*)
- z3_solve.py solve "dy/dt == 0"

Type	Method
Separable	Separate and integrate
Linear	Integrating factor e^{int P dx}
Exact	Find potential function
Bernoulli	Substitute v = y^{1-n}

Tool Commands

Track record

Benchmark

8 / 21

test cases passed, vs 13 / 21 without

Adoption

Users: 0
Times used: 0

Safety and source details

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 8/1/2026

View 15 scanner checks

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

vibeeval / vibecosystem

skills/math/odes-pdes/first-order-odes/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

More skills from the same source and nearby in the registry, with their headline benchmark lift.

Ready to supercharge your AI agents?

See it in action

What's inside

First Order Odes

When to Use

Decision Tree

Tool Commands

Track record

Benchmark

Adoption

SkillSafety

Source

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