Solving Homogeneous ODEs of Class C - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Differential Equations : Classifying ODEs : First Order : odeadvisor/homogeneousC

Solving Homogeneous ODEs of Class C

 

Description

Examples

Description

• 

The general form of the homogeneous equation of class C is given by the following:

homogeneousC_ode := diff(y(x),x)=F((a*x+b*y(x)+c)/(r*x+s*y(x)+t));

homogeneousC_ode:=ⅆⅆxyx=Fax+byx+crx+syx+t

(1)
  

where F is an arbitrary function of its argument. See Differentialgleichungen, by E. Kamke, p. 19. This type of ODE can be solved in a general manner by dsolve and the coefficients of the infinitesimal symmetry generator are also found by symgen.

Examples

withDEtools,odeadvisor,symgen

odeadvisor,symgen

(2)

odeadvisorhomogeneousC_ode

_homogeneous,class C,_dAlembert

(3)

A pair of infinitesimals for the homogeneousC_ode

symgenhomogeneousC_ode

_ξ=asxbrxbt+csasbr,_η=asybry+atcrasbr

(4)

The general solution for this ODE

ansdsolvehomogeneousC_ode

ans:=yx=atcr+RootOf∫_Z1F_aba_asr+_aⅆ_a+lnxasbrbt+cs+_C1xasbrbt+csas+br

(5)

Explicit or implicit results can be tested, in principle, using odetest

odetestans,homogeneousC_ode

0

(6)

See Also

DEtools

odeadvisor

dsolve

quadrature

linear

separable

Bernoulli

exact

homogeneous

homogeneousB

homogeneousC

homogeneousD

homogeneousG

Chini

Riccati

Abel

Abel2A

Abel2C

rational

Clairaut

dAlembert

sym_implicit

patterns

odeadvisor,types

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam