{"uid":"cap_Jy9yr1YbSSQm69K3hhCaA","slug":"numora-differential-equation-solver-3dc62fc4","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://numormo.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_pVmzqxyHDPh9yu0e1C8_K","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":"Solve the differential equation dy/dt = -0.5*y with initial value y0 = 100 over the time span from t=0 to t=20.","exampleUseCases":[{"title":"Exponential Decay Modeling","prompt":"I need to model radioactive decay — solve dy/dt = -0.03*y with an initial amount y0 = 500 over the time span from t=0 to t=100."},{"title":"Population Growth Simulation","prompt":"Can you numerically solve the logistic growth equation dy/dt = 0.2*y*(1 - y/1000) with y0 = 50 from t=0 to t=50?"},{"title":"RC Circuit Voltage Analysis","prompt":"Solve the ODE dy/dt = (5 - y) / 2 representing an RC circuit charging, starting at y0 = 0, from t=0 to t=10."}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T12:40:57.843Z","isFirstParty":false}