Solving Homogeneous ODEs of Class G - Maple Help

Online Help

All Products    Maple    MapleSim


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

Solving Homogeneous ODEs of Class G

 

Description

Examples

Description

• 

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

homogeneousG_ode := diff(y(x),x) = y(x)/x*F(y(x)/x^alpha);

homogeneousG_ode:=ⅆⅆxyx=yxFyxxαx

(1)
  

where F is an arbitrary functions of its argument. 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)

odeadvisorhomogeneousG_ode

_homogeneous,class G

(3)

A pair of infinitesimals for the homogeneousG_ode

symgenhomogeneousG_ode

_ξ=x,_η=yα

(4)

The general solution for this ODE

ansdsolvehomogeneousG_ode

ans:=yx=RootOflnx+_C1+∫_Z1_aα+F_aⅆ_axα

(5)

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

odetestans,homogeneousG_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