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Solving Homogeneous ODEs of Class B
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Description
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The general form of the homogeneous equation of class B is given by the following:
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homogeneousB_ode := F(diff(y(x),x), y(x)/x);
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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.
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Examples
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![[symgen]](/support/helpjp/helpview.aspx?si=7208/file04373/math34.png)
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A pair of infinitesimals for homogeneousB_ode
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![[_xi = x, _eta = y]](/support/helpjp/helpview.aspx?si=7208/file04373/math43.png)
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The general solution for this ODE
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Explicit or implicit results can be tested, in principle, using odetest:
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See Also
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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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