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DEtools

  

reduceOrder

  

apply the method of reduction of order to an ODE

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

reduceOrder(des, dvar, partsol, solutionForm)

Parameters

des

-

ordinary differential equation, or its list form

dvar

-

the dependent variable for an equation

partsol

-

partial solution, or list of partial solutions

solutionForm

-

flag to indicate the DE should be solved explicitly

Description

• 

Important: The DEtools[reduceOrder] command has been deprecated. Use the superseding command DEtools[reduce_order] instead.

• 

This routine is used to either a) return an ODE of reduced order or b) solve the ODE explicitly by the method of reduction of order, given a partial (particular) solution of the ODE.  Without the optional flag basis, a reduced ODE is returned.  If basis appears as the fifth argument, then a list containing the basis of the solution is returned.  Note that a solution basis may contain DESol data structures.

• 

des may be input as an explicit ODE, as a list of coefficients (in the case of the ODE being homogeneous), or in the form returned by convertAlg for the non-homogeneous case.

• 

partsol may be a single partial solution, or a list of partial solutions.  Note that it is assumed all given partial solutions are correct and valid.  When a reduced ODE is to be returned, the order of the resulting ODE will be equal to the order of the original less the number of partial solutions given.

• 

The command with(DEtools,reduceOrder) allows the use of the abbreviated form of this command.

Examples

Important: The DEtools[reduceOrder] command has been deprecated. Use the superseding command DEtools[reduce_order] instead.

withDEtools:

deⅆ3ⅆx3yx6ⅆ2ⅆx2yx+11ⅆⅆxyx6yx

de:=ⅆ3ⅆx3yx6ⅆ2ⅆx2yx+11ⅆⅆxyx6yx

(1)

solⅇx

sol:=ⅇx

(2)

reduceOrderde,yx,sol

ⅆ2ⅆx2yx3ⅆⅆxyx+2yx

(3)

reduceOrderde,yx,sol,basis

ⅇx,ⅇ2x,12ⅇ3x

(4)

de224,50,35,10,1

de2:=24,50,35,10,1

(5)

sol1ⅇx

sol1:=ⅇx

(6)

sol2ⅇ2x

sol2:=ⅇ2x

(7)

reduceOrderde2,yx,sol1

6,11,6,1

(8)

reduceOrderde2,yx,sol2

2,1,2,1

(9)

reduceOrderde2,yx,sol1,sol2

2,3,1

(10)

reduceOrderde2,yx,sol1,sol2,basis

ⅇx,ⅇ2x,12ⅇ3x,16ⅇ4x

(11)

de3x9+x3ⅆ3ⅆx3yx+18x8ⅆ2ⅆx2yx90xⅆⅆxyx3011x63yx

de3:=x9+x3ⅆ3ⅆx3yx+18x8ⅆ2ⅆx2yx90xⅆⅆxyx3011x63yx

(12)

solxx6+1

sol:=xx6+1

(13)

reduceOrderde3,yx,sol

x2ⅆ2ⅆx2yx+3xⅆⅆxyx90yx

(14)

reduceOrderde3,yx,sol,basis

xx6+1,191x91x91x6+1,191x91x91x6+1

(15)

See Also

DESol

DEtools

DEtools[convertAlg]

DEtools[reduce_order]

dsolve

 


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