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Solving Exact ODEs
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Description
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The general form of the exact ODE is given by:
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exact_ode := D[2](C)(x,y(x))*diff(y(x),x)+D[1](C)(x,y(x))=0;
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)(x, y(x))*(diff(y(x), x))+(D[1](C))(x, y(x)) = 0](/support/helpjp/helpview.aspx?si=6698/file04368/math17.png)
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where C is an arbitrary function of its arguments. See Kamke's book, p. 28. This type of ODE can be solved in a general manner by dsolve, and the infinitesimals can also be determined by symgen.
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Examples
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![[odeadvisor, symgen, symtest]](/support/helpjp/helpview.aspx?si=6698/file04368/math36.png)
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![[_exact, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]](/support/helpjp/helpview.aspx?si=6698/file04368/math43.png)
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Implicit or explicit results can be tested using odetest
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A pair of infinitesimals for exact_ode are given by
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![sym := [_xi = 0, _eta = 1/(diff(C(x, y), y))]](/support/helpjp/helpview.aspx?si=6698/file04368/math71.png)
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Symmetries can be tested as well using symtest
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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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