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Home : Support : Online Help : Mathematics : Discrete Mathematics : Combinatorics : gfun : gfun/diffeqtohomdiffeq

gfun

  

diffeqtohomdiffeq

  

make a differential equation homogeneous

  

rectohomrec

  

make a recurrence homogeneous

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

diffeqtohomdiffeq(deq, y(z))

rectohomrec(rec, u(n))

Parameters

deq

-

linear differential equation in y(z) with polynomial coefficients

y

-

name; differential equation function

z

-

name; variable of the differential equation function y

rec

-

linear recurrence with polynomial coefficients

u

-

name; recurrence name

n

-

name; index of the recurrence u

Description

• 

The diffeqtohomdiffeq(deq, y(z)) command makes the differential equation, deq homogeneous.

  

If deq is not homogeneous, the diffeqtohomdiffeq function produces a differential equation of order increased by one which is homogeneous and cancels all the solutions of the original equation.

  

If deq is homogeneous, it is unchanged.

• 

The rectohomrec(rec, u(n)) command makes the recurrence, rec, homogeneous.

  

If rec is not homogeneous, the rectohomrec function produces a recurrence of order increased by one which is homogeneous and cancels all the solutions of the original equation.

  

If rec is homogeneous, it is unchanged.

Examples

withgfun:

deqⅆⅆxyxx1+2yx2x3:

diffeqtohomdiffeqdeq,yx

4yx+4x11ⅆⅆxyx+2x2x+3ⅆ2ⅆx2yx

(1)

diffeqtohomdiffeqdeq,y0=2,yx

4yx+4x11ⅆⅆxyx+2x2x+3ⅆ2ⅆx2yx,y0=2,Dy0=1

(2)

recun+1=un+n2+1:

rectohomrecrec,un

n22n2un+2n2+2n+3un+1+n21un+2

(3)

rectohomrecrec,u0=1,un

n22n2un+2n2+2n+3un+1+n21un+2,u0=1,u1=2

(4)

See Also

diff

gfun

 


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