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Solving Homogeneous ODEs of Class C
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Description
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The general form of the homogeneous equation of class C is given by the following:
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homogeneousC_ode := diff(y(x),x)=F((a*x+b*y(x)+c)/(r*x+s*y(x)+t));
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where F is an arbitrary function of its argument. 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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![[odeadvisor, symgen]](/support/helpjp/helpview.aspx?si=7209/file04374/math34.png)
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![[[_homogeneous, `class C`], _dAlembert]](/support/helpjp/helpview.aspx?si=7209/file04374/math41.png)
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A pair of infinitesimals for the homogeneousC_ode
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![[_xi = (-b*r*x-b*t+s*a*x+s*c)/(-b*r+s*a), _eta = (a*s*y+a*t-r*b*y-r*c)/(-b*r+s*a)]](/support/helpjp/helpview.aspx?si=7209/file04374/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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