classify_ode ( eq, func = None, dict = False, ics = None, *, prep = True, xi = None, eta = None, n = None, ** kwargs ) # May be divided further so that the divided systems may have coefficient matrix with commutative antiderivative. Those which have either a coefficient matrix with a commutative antiderivative or those systems which The dependent variable and RHS is an expression in terms of the independent variable.Īmong the non constant coefficient types, not all the systems are solvable by this function. Each solution is a list of equations where LHS is This function returns a list of solutions. thisįunction can solve the above types irrespective of the number of equations in the system passed.īut, the bigger the system, the more time it will take to solve the system. The types of systems described above are not limited by the number of equations, i.e. Any higher order linear system of ODEs that can be reduced to one of the 5 forms of systems described above. Any implicit system which can be divided into system of ODEs which is of the above 4 formsĦ. Linear, First Order, non-constant coefficient non-homogeneous system of ODEsĥ. Linear, First Order, non-constant coefficient homogeneous system of ODEsĤ. Linear, First Order, Constant coefficient non-homogeneous system of ODEsģ. Linear, First Order, Constant coefficient homogeneous system of ODEsĢ. It is solvable by this function, and returns the solution if found any.ġ. This function takes a system of ODEs as an input, determines if the When the parameters passed are not in the required form. Solves any(supported) system of Ordinary Differential Equations Parameters : dsolve_system ( eqs, funcs = None, t = None, ics = None, doit = False, simplify = True ) # ics is the set of initial/boundary conditions for the differential equation. Infinitesimals() with the help of various Nothing is specified, xi and eta are calculated using The user can specify values for the infinitesimals. Of point transformations for which the differential equation is They are the infinitesimals of the Lie group xi and eta are the infinitesimal functions of an ordinaryĭifferential equation. Note that the solution mayĬontain more arbitrary constants than the order of the ODE with Solutions for func or simplification of arbitrary constants. Turn this off, for example, to disable solving of Hints below for more options that you can use for hint. The default hint, default, will use whatever hint is UseĬlassify_ode(eq, f(x)) to get all of the possible hints for an hint is the solving method that you want dsolve to use. Many cases it is not necessary to provide this it will beĪutodetected (and an error raised if it could not be detected). Variable make up the ordinary differential equation eq. f(x) is a function of one variable whose derivatives in that Or an expression, which is assumed to be equal to 0. Eq can be any supported ordinary differential equation (see the
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