Solving Homogeneous ODEs of Class B - Maple Help

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Solving Homogeneous ODEs of Class B

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

ans:=dsolvehomogeneousB_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, 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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