Solving Homogeneous ODEs of Class G - Maple Help

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Solving Homogeneous ODEs of Class G

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

ans:=dsolvehomogeneousG_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, and ?odeadvisor,<TYPE> where <TYPE> is one of: quadrature, linear, separable, Bernoulli, exact, homogeneous, homogeneousB, homogeneousC, homogeneousD, homogeneousG, Chini, Riccati, Abel, Abel2A, Abel2C, rational, Clairaut, dAlembert, sym_implicit, patterns; for other differential orders see odeadvisor,types.


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