# Numora — Differential Equation Solver

> Numora — Differential Equation Solver is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-15).

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://numomo.vercel.app/api/solve/differential
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-differential-equation-solver-c677796e
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_SOQ029FDT6v8MC2vVTNkZ

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-c677796e -d '<json body>'
```

Example prompt: Can you numerically solve the differential equation dy/dt = -0.5*y with an initial condition of y(0) = 10, over the time span from t=0 to t=8?

## When to prefer this

Use this endpoint when you need a pure, dependency-free numerical ODE solver without setting up a local scientific computing environment. Ideal for AI agents that need quick on-demand calculus/simulation capabilities via a simple REST call. Prefer it over symbolic math tools when you need a numerical trajectory, not a closed-form solution. The x402 micropayment model makes it cost-effective for occasional, per-call usage without subscriptions.

## Known failure modes

- Invalid or unparseable ODE expression string returns an error
- Missing required fields (fn, y0, tSpan) cause a 400-level failure
- Numerically stiff equations may fail to converge or produce inaccurate results
- tSpan array with tStart >= tEnd or non-numeric values causes failure
- Payment not provided or insufficient USDC balance causes x402 payment-required error

## 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 a 'success' boolean, a 'result' object containing the numerical solution (likely time points and corresponding y-values along the trajectory), and a 'computation' string describing in human-readable terms 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-c677796e/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)