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Home : Support : Online Help : Mathematics : Differential Equations : DEtools : Linear DE Manipulation : DEtools/translate

DEtools

  

translate

  

translate a DE or operator list centered on 0 to one centered on a point

  

untranslate

  

translate a DE or operator list centered on a point to one centered on 0

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

translate(des, ivar, pt, dvar)

untranslate(des, ivar, pt, dvar)

Parameters

des

-

differential equation, or differential operator list

ivar

-

independent variable

pt

-

point of translation

dvar

-

dependent variable, in the case of a DE

Description

• 

The routines translate and untranslate are used for the translation of DEs and operators.  In the case of a linear differential operator, the input des is given by a list (here A), which defines the operator by

L  |  Ly=A1yx+A2y' x+...+An+1ⅆnⅆxnyx

• 

The routine translate takes a DE or linear operator in the independent variable ivar, assumed to be centered about 0, and translates it to a DE or operator centered about pt.  Essentially, translate acts like DEtools[Dchangevar] for the restricted cases t=1x (pt = infinity) and t=x+pt (otherwise).

• 

Likewise, the routine untranslate takes a DE, operator, or DE solution that is centered on the point pt and translates it to the equivalent centered on 0.

• 

dvar must be provided in the instance that des is a differential equation or DE solution.  It is not required if des is an operator list.

• 

Results may be "normalized" by way of DEtools[DEnormal].

• 

Linear differential operators may be derived from DEs by way of DEtools[convertAlg].

• 

These functions are part of the DEtools package, and so they can be used in the form translate(..) and untranslate(..) only after executing the command with(DEtools). However, they can always be accessed through the long form of the command DEtools[translate](..) or DEtools[untranslate](..).

Examples

withDEtools:

Linear differential operator

L_A1xx5+2x+2,x2+1,x5+2x+2:

a1translateL_A,x,∞

a1x62x5+2x4+1,4x5+3x4x2+2x2,2x5+2x4+1x

(1)

a2untranslatea1,x,∞

a21xx5+2x+2,x2+1,x5+2x+2

(2)

Differential equation

DE212x3+3x25x+2yx+42x2x+1xx1Dyx+50x3x13D2yx=xsinx:

de1translateDE,x,a,yx

de1212x+a3+3x+a25x5a+2yx+42x+a2xa+1x+ax+a1Dyx+50x+a3x+a13D2yx=x+asinx+a

(3)

de2untranslatede1,x,a,yx:

de2DEnormalde2,x,yx

de250x6150x5+150x450x3ⅆ2ⅆx2yx+42x484x3+84x242xⅆⅆxyx42yxx3+63yxx2105yxx+42yx=xsinx

(4)

See Also

DEtools

DEtools[convertAlg]

DEtools[DEnormal]