Exercise · ZW-DIRECTION-FIELD-001 · ★☆☆ Basic
For \(y'=x+y\), what slope does the field segment have at the point \((1,2)\)?
Choose one option.
Show answer
- A. \(3\)
Explanation
The slope at a point is \(f(x,y)\): \(1+2=3\).
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
- ZW-DIRECTION-FIELD-002 For y'=xy, what slope does the segment have at (2,-1)?
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- ZW-DIRECTION-FIELD-005 Which equation produces a field with all segments parallel?
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- ZW-DIRECTION-FIELD-007 The solutions of y'=-x/y are circles x^2+y^2=C. What slope does the field segment have at (3,4)?
- ZW-DIRECTION-FIELD-008 In the field of y'=y^2-4, which horizontal lines are constant solutions?
- ZW-DIRECTION-FIELD-009 For y'=x-y, the line y=x-1 is the isocline of slope 1. Is it also a solution of the equation?