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autonomous

  

determine if a set of DEs is strictly autonomous

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

autonomous(des, vars, ivar)

Parameters

des

-

list or set of differential equations

vars

-

list or set of dependent variables

ivar

-

independent variable

Description

• 

This routine is used to determine if a system of differential equations, or a single differential equation, is strictly autonomous.  "Strictly" means that the independent variable does not appear as a part or argument of any terms, other than in calls to 'diff' or 'D', or when explicitly defined as part of the dependent variable.

• 

'true' is returned if the system is determined to be autonomous by the above criteria; otherwise, 'false' is returned.

• 

There can be only one independent variable.

• 

This function is part of the DEtools package, and so it can be used in the form autonomous(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[autonomous](..).

Examples

withDEtools:

DEⅆⅆxyx=yxsinyxcossintanBesselyxyx12,3

DEⅆⅆxyx=yxsinyx+cossintanBesselyxyx,3

(1)

autonomousDE,yx,x

true

(2)

autonomoussinztzt2D4ztcoszt5,z,t

true

(3)

DE2ⅆⅆsxsxscosarctanxs=arctans

DE2ⅆⅆsxsxs1+xs2=arctans

(4)

autonomousDE2,x,s

false

(5)

DE3ⅆⅆxyx=sinyxzx,ⅆⅆxzxcoszx=yxBesselyx,3

DE3ⅆⅆxyx=sinyxzx,ⅆⅆxzxcoszx=yxBesselyx,3

(6)

autonomousDE3,y,z,x

true

(7)

See Also

DEplot

DEtools

DEtools[phaseportrait]

dfieldplot