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DEtools

  

abelsol

  

find solutions to a first order Abel ODE

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

abelsol(lode, v)

Parameters

lode

-

first order differential equation

v

-

dependent variable of the lode

Description

• 

An Abel ODE is a first order ODE of the form

  

 y'x=f0x+f1xyx+f2xyx2+f3xyx3 

• 

The abelsol routine determines whether the first argument is a first order Abel ODE and, if so, attempts to find a closed form solution.

• 

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 abelsol(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[abelsol](..).

Examples

withDEtools:

odeⅆⅆxyx=a0+a1yx+a2yx2+a3yx3

odeⅆⅆxyx=a0+a1yx+a2yx2+a3yx3

(1)

abelsolode,yx

yx=27RootOf3a1a3x+a22x+81_Z3a1a3a223729_a3a02a34486_a3a0a1a2a33+108_a3a0a23a32+81_a3a12a22a3236_a3a1a24a3+4_a3a26+729_aa13a33729_aa12a22a32+243_aa1a24a327_aa26729a13a33+729a12a22a32243a1a24a3+27a26ⅆ_aa3+3_C1a3a0a329RootOf3a1a3x+a22x+81_Z3a1a3a223729_a3a02a34486_a3a0a1a2a33+108_a3a0a23a32+81_a3a12a22a3236_a3a1a24a3+4_a3a26+729_aa13a33729_aa12a22a32+243_aa1a24a327_aa26729a13a33+729a12a22a32243a1a24a3+27a26ⅆ_aa3+3_C1a3a1a2a3+2RootOf3a1a3x+a22x+81_Z3a1a3a223729_a3a02a34486_a3a0a1a2a33+108_a3a0a23a32+81_a3a12a22a3236_a3a1a24a3+4_a3a26+729_aa13a33729_aa12a22a32+243_aa1a24a327_aa26729a13a33+729a12a22a32243a1a24a3+27a26ⅆ_aa3+3_C1a3a23+9a2a1a33a239a33a1a3a22

(2)

odeDzt+3azt3+6atzt2

odeDzt+3azt3+6atzt2

(3)

abelsolode,zt

zt=13at2+RootOfAiryBi_Z3a13_C1t+3a13tAiryAi_Z+AiryBi1,_Z_C1+AiryAi1,_Z3a13

(4)

See Also

DEtools

dsolve