ODE Sketch Lab · draw two curves, find the one ODE can live with

1) Sketch y(x) on the left.   2) Sketch its derivative y′(x) on the right.
3) Pick the ODE.   4) Press Reconcile.   5) Tune the branch.
y(x) — your solution sketch pencil · ink #222
points stored: 0 family branch: — residual ‖y'−dy/dx‖: —
y′(x) — claimed derivative dashed · ink #7a3b2e
points stored: 0 ODE target RHS: y residual ‖y′−RHS‖: —

Branch picker — which of the reconciled solutions do you keep?

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your y(x) your y′(x) filtered ȳ(x) filtered ȳ′(x) branch solution Y(x; C)
The filter is a one-shot alternating projection: ȳ′ ← RHS(ȳ) then ȳ ← antiderivative(ȳ′). We borrow a "branch" constant so you can explore the family of ODE-consistent solutions nearest your doodle. Drag the slider to flip between principal (the unique solution through your starting point) and the alternative branch (won by C, the doodle's own ± sign).