# Numora Differential Equation Solver

> Numora Differential Equation Solver is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.05/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://numorapoi.orbonomy.xyz/api/solve/differential
- Price: $0.05/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-e8f0619f
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_d7SjAXNCTQnUuq6ZCrROg

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-e8f0619f -d '<json body>'
```

Example prompt: Solve the differential equation dy/dt = -0.5*y with initial value y(0) = 10 over the time span from t=0 to t=20.

## When to prefer this

Choose this endpoint when you need pure server-side numerical ODE solving without setting up a local math library or scientific computing environment. Ideal for AI agents needing quick, on-demand solutions to first-order initial value problems with a known f(t,y) expression, especially in serverless or lightweight contexts where dependencies like SciPy or MATLAB are unavailable.

## Known failure modes

- Invalid ODE expression syntax — returns error if fn string cannot be parsed or evaluated
- Missing required fields (fn, y0, or tSpan) — returns validation error
- tSpan array malformed or tStart >= tEnd — returns error
- Stiff or numerically unstable ODE may fail to converge — returns computation error
- Payment failure or insufficient USDC balance — returns 402 Payment Required

## 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 flag, a result object containing the numerical solution (typically time points and corresponding y values), and a human-readable computation description string explaining what was computed.

## 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-e8f0619f/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)