How do I simulate a differential equation?

Open this page and use the live Eigenvectors 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 Eigenvectors

Eigenvectors for a differential equation

Simulate a differential equation live in your browser. This runs the real Eigenvectors 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

Eigenvector VisualizerLive

2×2 linear transformation

Controls

A matrix warps the unit circle into an ellipse. Eigenvectors are the special directions that only stretch — never rotate — by their eigenvalue.

Presets

▶ Run in Python

Data Inspector

det3.00

trace4.00

λ₁3.00

λ₂1.00

Governing equation

A = [2.0 1.0 1.0 2.0], A v = λ v, det (A - λ I) = 0, λ = 3.00, 1.00

Reading this result: Symmetric matrix (b = c): its eigenvectors meet at right angles, so the ellipse axes line up exactly with the green and pink lines.

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

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About this simulation

The full Eigenvectors 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 Eigenvectors

Eigenvectors for compound interest Eigenvectors for a population curve Eigenvectors for a loan payoff Eigenvectors for a logistic map Eigenvectors for a Fibonacci sequence Eigenvectors for a fractal tree Eigenvectors for a Fourier series Eigenvectors 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 Eigenvectors 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.