# Numora Differential Equation Solver

> Numora Differential Equation Solver is a paid API for AI agents from numormo.vercel.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://numormo.vercel.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-3dc62fc4
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Jy9yr1YbSSQm69K3hhCaA

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-3dc62fc4 -d '<json body>'
```

Example prompt: Solve the differential equation dy/dt = -0.5*y with initial value y0 = 100 over the time span from t=0 to t=20.

## When to prefer this

Choose 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, with no external dependencies. Ideal for scientific computing, physical simulations, financial modeling, or any agent workflow requiring differential equation solutions as a pure computation step without standing up a local math library.

## Known failure modes

- Invalid ODE expression string that cannot be parsed — returns error
- tSpan array not formatted as [tStart, tEnd] — returns validation error
- Stiff or chaotic ODE causing numerical instability — may return incomplete or inaccurate results
- Missing required fields (fn, y0, tSpan) — returns 400-level error
- Micropayment failure (insufficient USDC balance) — request rejected before computation

## 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 (typically arrays of time points and corresponding y values), and a 'computation' string describing in human-readable form 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-3dc62fc4/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormo.vercel.app](https://www.zero.xyz/host/numormo.vercel.app/llms.txt)