Solving Homogeneous ODEs of Class B - Maple Programming Help

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Solving Homogeneous ODEs of Class B

 

Description

Examples

Description

• 

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

homogeneousB_ode := F(diff(y(x),x), y(x)/x);

homogeneousB_ode:=Fⅆⅆxyx,yxx

(1)
  

where F is an arbitrary functions of its arguments. 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,symgen

symgen

(2)

A pair of infinitesimals for homogeneousB_ode

symgenhomogeneousB_ode

_ξ=x,_η=y

(3)

The general solution for this ODE

ansdsolvehomogeneousB_ode

ans:=yx=RootOf∫_Z1RootOfF_Z,_a_aⅆ_a+lnx+_C1x

(4)

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

odetestans,homogeneousB_ode

0

(5)

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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