{"uid":"cap_d7SjAXNCTQnUuq6ZCrROg","slug":"numora-differential-equation-solver-e8f0619f","name":"Numora Differential Equation Solver","description":"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.","url":"https://numorapoi.orbonomy.xyz/api/solve/differential","method":"POST","headers":{},"bodySchema":{"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]"}}},"responseSchema":{"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"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.05/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.05","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.05","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_uwel7lB4Onw3PLaAu-PUx","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.05","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Numerically solves ordinary differential equations (ODEs) of the form dy/dt = f(t,y) given an initial condition and time span","exampleAgentPrompt":"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.","exampleUseCases":null,"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T19:03:42.000Z","isFirstParty":false}