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Solving Homogeneous ODEs of Class G
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Description
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The general form of the homogeneous equation of class G is given by the following:
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homogeneousG_ode := diff(y(x),x) = y(x)/x*F(y(x)/x^alpha);
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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.
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Examples
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![[odeadvisor, symgen]](/support/helpjp/helpview.aspx?si=7211/file04376/math34.png)
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![[[_homogeneous, `class G`]]](/support/helpjp/helpview.aspx?si=7211/file04376/math41.png)
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A pair of infinitesimals for the homogeneousG_ode
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![[_xi = x, _eta = y*alpha]](/support/helpjp/helpview.aspx?si=7211/file04376/math50.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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