{"uid":"cap_SOQ029FDT6v8MC2vVTNkZ","slug":"numora-differential-equation-solver-c677796e","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://numomo.vercel.app/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":"registry","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":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm__-V4flJjdyMyMqst9uh7g","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"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":"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?","exampleUseCases":[{"title":"Exponential decay simulation","prompt":"Solve the ODE dy/dt = -0.3*y with y(0) = 100 from t=0 to t=20 — I want to model radioactive decay over time."},{"title":"Logistic population growth model","prompt":"I need to numerically integrate dy/dt = 0.4*y*(1 - y/500) with an initial population of y(0) = 10 from t=0 to t=30."},{"title":"Cooling curve over time","prompt":"Can you solve dy/dt = -0.1*(y - 20) with y(0) = 90 over the interval t=0 to t=60? I'm modeling Newton's law of cooling."}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T18:56:36.431Z","isFirstParty":false}