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First-order ODEs (Separable & Linear) + Direction Field

Solve separable and linear first-order ODEs in one interface: slope field, solution curves, Simpson integrals, integrating factor, numeric inversion, RK4 check, CSV export, and shareable URLs.

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Inputs

Initial condition (x0, y0)
Window [x_min, x_max, y_min, y_max]
Field grid (Nx×Ny)
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Curve samples

First-order ODEs

We show Simpson integrals, integrating factor, numeric inversion, RK4 error, CSV, and shareable URLs.

Tip: click the canvas to add an initial condition at that point.

Result

How it’s calculated

    Teacher notes

    FAQ

    How is the direction field rendered?

    We evaluate the slope on a uniform grid of x and y, clip extreme gradients, and draw short segments so the field stays legible. RK4 runs on the same field to verify the main solution curve.

    How do you stabilise the numeric inversion?

    For separable equations we scan [y_min, y_max] for a sign change and refine with bisection. Linear equations rely on the integrating factor, and we expose the RK4 discrepancy to monitor the residual error.