# Numora Differential Equation Solver

> Numora Differential Equation Solver is a paid API for AI agents from numormor.netlify.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-14).

Numerically solves ordinary differential equations (ODEs) of the form dy/dt = f(t,y) given an initial condition and time span

## Facts

- Endpoint: POST https://numormor.netlify.app/api/solve/differential
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-differential-equation-solver-81cf4379
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_ZagMXhKAJJ8A7nsqZIHmV

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-differential-equation-solver-81cf4379 -d '<json body>'
```

Example prompt: Can you solve the differential equation dy/dt = -0.5 * y with initial condition y(0) = 10 over the time span from t=0 to t=20?

## When to prefer this

Use this endpoint when you need to numerically solve a first-order ODE (dy/dt = f(t,y)) with a known initial condition over a defined time interval, without setting up any local computation environment. Ideal for AI agents needing on-demand calculus computation with no dependencies.

## Known failure modes

- Invalid or unparseable ODE expression string returns error
- Missing required fields (fn, y0, tSpan) returns validation error
- tSpan array not in [tStart, tEnd] format causes failure
- Stiff or numerically unstable ODE may produce inaccurate or failed results
- Non-numeric y0 or tSpan values cause parsing errors
- Payment failure via x402 micropayment protocol blocks request

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with success=true, a result object containing the numerical solution (time points and corresponding y values), and a human-readable computation string describing what was solved.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "fn",
  "y0",
  "tSpan"
 ],
 "properties": {
  "fn": {
   "type": "string",
   "description": "ODE expression dy/dt = f(t,y)"
  },
  "y0": {
   "type": "number"
  },
  "tSpan": {
   "type": "array",
   "description": "[tStart, tEnd]"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-differential-equation-solver-81cf4379/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormor.netlify.app](https://www.zero.xyz/host/numormor.netlify.app/llms.txt)