Direction Fields

A direction field shows the slope of the DE \(y^{'} = f(x,y)\) at each point \((x,y)\). The figure below shows an example direction field. At each point \((x,y)\), a lineal element is shown depicting the slope. The three solutions below follow the direction of the fields for different particular solutions.

Sketch the direction field for the equation \( \frac{dy}{dx}=-2xy \). Sketch the solutions subject to \(y(0)=3\).

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