Exercise · ZW-DIRECTION-FIELD-010 · ★★★ Advanced

With \(y'=x+y\) and \(y(0)=1\), follow the field with horizontal steps of \(0.1\) (use the slope at the start of each step). What is the estimate of \(y(0.2)\)?

Choose one option.

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  • A. \(1.22\)

Explanation

At \((0,1)\) the slope is \(1\), so \(y(0.1)\approx 1.1\). At \((0.1,1.1)\) the slope is \(1.2\), so \(y(0.2)\approx 1.1+0.12=1.22\). Reusing the first slope would give the typical error \(1.20\).

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Review the concept: Direction field

A direction field draws, at many points of the plane, a small segment with the slope that the differential equation assigns to that point.

\[\text{slope at }(x,y)=f(x,y)\]

More practice problems: direction field

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