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Solving Homogeneous ODEs of Class D
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Description
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The general form of the homogeneous equation of class D is given by the following:
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homogeneousD_ode := diff(y(x),x)= y(x)/x+g(x)*f(y(x)/x);
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where f(y(x)/x) and g(x) are arbitrary functions of their arguments. See Differentialgleichungen, by E. Kamke, p. 20. 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, symtest]](/support/helpjp/helpview.aspx?si=7210/file04375/math34.png)
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![[[_homogeneous, `class D`]]](/support/helpjp/helpview.aspx?si=7210/file04375/math41.png)
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A pair of infinitesimals for homogeneousD_ode
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![[_xi = x/g(x), _eta = y/g(x)]](/support/helpjp/helpview.aspx?si=7210/file04375/math50.png)
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The general solution for this ODE
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Answers can be tested using odetest
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Let's see how the answer above works when turning f into an explicit function; f is the identity mapping.
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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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