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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_odeⅆⅆxyx=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

with(DEtools, odeadvisor, symgen);

odeadvisor,symgen

(2)

odeadvisor(homogeneousC_ode);

_homogeneous,class C,_dAlembert

(3)

A pair of infinitesimals for the homogeneousC_ode

symgen(homogeneousC_ode);

_ξ=asxbrxbt+csasbr,_η=asybry+atcrasbr

(4)

The general solution for this ODE

ans := dsolve(homogeneousC_ode);

(5)

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

odetest(ans,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

 


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