Differential Equations

Euler's Method — Numerical ODE Approximation

Approximate y(x) using yₙ₊₁ = yₙ + h · f(xₙ, yₙ). Build a step-by-step iteration table and compare against the exact solution where available.

Live Calculator · Step-by-Step · Differential Equations

Inputs

f(x, y) = dy/dx

x₀ (start)

y₀ = y(x₀)

x_end

Step size h

Result

Euler Formula

yₙ₊₁ = yₙ + h · f(xₙ, yₙ)

Approximate y(x_end)

—

Exact y(x_end)

—

Global Error

—

Iteration Table

Configure inputs above.

Euler Path vs Exact Solution

Put It Into Practice

The calculator shows the steps — a quiz proves you can do them on your own.

Alexander tutors all math and CS levels — $55/session, free consultation.