How do I simulate a differential equation?

Open this page and use the live Direction Field tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a differential equation from your own measurements.

Use case · powered by Direction Field

Direction Field for a differential equation

Simulate a differential equation live in your browser. This runs the real Direction Field solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

For:Students Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders

Direction Field / Slope FieldLive

dy/dx = f(x, y) · drag the start point

Controls

dy/dx = f(x, y)

▶ Run in Python

Data Inspector

Equationdy/dx = f(x,y)

Curves1

IntegratorRK2

Governing equation

\frac{d y}{d x} = f (x, y) = y - x

Reading this result: Every tick shows the slope dy/dx = f(x,y) at that point; drag the start point and RK2 rethreads the solution curve live, always staying tangent to the arrows. That start point alone picks which one curve you get — click elsewhere to pin extra curves for comparison.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

About this simulation

The full Direction Field tool models a differential equation with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

More you can do with Direction Field

Direction Field for compound interest Direction Field for a population curve Direction Field for a loan payoff Direction Field for a logistic map Direction Field for a Fibonacci sequence Direction Field for a fractal tree Direction Field for a Fourier series Direction Field for a Taylor approximation

Other ways to simulate a differential equation

Visual Node Graph for a differential equation Symbolic Math for a differential equation Vector Fields for a differential equation Notebook for a differential equation Fractal Explorer for a differential equation Fourier Series for a differential equation

Frequently asked questions

How do I simulate a differential equation?: Open this page and use the live Direction Field tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a differential equation from your own measurements.