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DEtools

  

mutest

  

test a given integrating factor

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

mutest(mu, ODE, y(x))

Parameters

mu

-

integrating factor

ODE

-

ordinary differential equation

y(x)

-

(optional) indeterminate function of the ODE

Description

• 

The mutest command checks whether a given expression is an integrating factor of a given ODE. Similar to odetest, mutest returns 0 when the first argument - say mu - is indeed an integrating factor.  Otherwise it returns an algebraic expression obtained after simplifying the Exactness condition. This Exactness condition is obtained by applying Euler's operator (satisfied by total derivatives) to mu times the ODE.

• 

Note however that when the result returned by mutest is not zero, the expression might nevertheless be an integrating factor. In some cases you can obtain the desired 0 with further simplifications by using commands such as expand and combine.

• 

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

Examples

A first order ODE

withDEtools:

ODEⅆⅆxyx=yxax+bx

ODE:=ⅆⅆxyx=yxax+bx

(1)

An integrating factor for ODE above

ΜintfactorODE

Μ:=ⅇ∫axⅆx

(2)

Testing this integrating factor

mutestΜ,ODE

0

(3)

A second order ODE example

ODEⅆ2ⅆx2yx=ⅆⅆxyx2+2xⅆⅆxyx+2yxyx

ODE:=ⅆ2ⅆx2yx=ⅆⅆxyx2+2xⅆⅆxyx+2yxyx

(4)

Μ1ⅆⅆxyx+2x

Μ:=1ⅆⅆxyx+2x

(5)

mutestΜ,ODE

0

(6)

See Also

DEtools

dsolve

firint

intfactor

PDEtools

redode

 


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