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单词 Isocline
释义

isocline


Let Γ be a family of plane curves.  The isocline of Γ is the locus of the points, in which all members of Γ have an equal slope.

If the family Γ has the differential equationMathworldPlanetmath

F(x,y,dydx)=0,

then the equation of any isocline of Γ has the form

F(x,y,K)=0

where K is .

For example, the family

y=eCx

of exponentialPlanetmathPlanetmath (http://planetmath.org/ExponentialFunction) curves satisfies the differential equation  dydx=CeCx  or  dydx=Cy,  whence the isoclines are  Cy=K,  i.e. they are horizontal lines.

http://en.wikibooks.org/wiki/Differential_Equations/Isoclines_1Wiki

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更新时间:2025/5/3 12:21:12