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DEtools

  

liesol

  

find solutions of a first order Lie ODE

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

liesol(lode, v)

Parameters

lode

-

first order differential equation

v

-

dependent variable of the lode

Description

• 

The liesol routine attempts to find a solution to the equation by using Lie methods. See dsolve,Lie.

• 

The first argument is a differential equation in diff or D form and the second argument is the function in the differential equation.

• 

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

Examples

withDEtools:

A nonlinear fifth order example (number 17 from Kamke's book) solved by reducing the order constructively using canonical coordinates

ode9ⅆ2ⅆx2yx2ⅆ5ⅆx5yx45ⅆ2ⅆx2yxⅆ3ⅆx3yxⅆ4ⅆx4yx+40ⅆ3ⅆx3yx

ode9ⅆ2ⅆx2yx2ⅆ5ⅆx5yx45ⅆ2ⅆx2yxⅆ3ⅆx3yxⅆ4ⅆx4yx+40ⅆ3ⅆx3yx

(1)

liesolode,yx

yx=∫∫RootOf∫_Z1RootOf20ln_f+∫_Z_kⅇRootOf81_k2ⅇ_Z40ⅇ_Zln220ⅇ_Zln5+20ⅇ_Zlnⅇ_Z+27+162_C1ⅇ_Z20_Zⅇ_Z+2187_k21080ln2540ln5+540lnⅇ_Z+27+4374_C1540_Z540+27ⅆ_k+20_C2ⅆ_f+x+_C3ⅆxⅆx+_C4x+_C5

(2)

See Also

DEtools

dsolve

dsolve,Lie