Solving Exact ODEs - Maple Help

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Solving Exact ODEs

Description

• 

The general form of the exact ODE is given by:

exact_ode := D[2](C)(x,y(x))*diff(y(x),x)+D[1](C)(x,y(x))=0;

exact_ode:=D2Cx,yxⅆⅆxyx+D1Cx,yx=0

(1)
  

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.

Examples

withDEtools,odeadvisor,symgen,symtest

odeadvisor,symgen,symtest

(2)

odeadvisorexact_ode

_exact,_1st_order,_with_symmetry_[F(x),G(y)]

(3)

ans:=dsolveexact_ode

ans:=Cx,yx+_C1=0

(4)

Implicit or explicit results can be tested using odetest

odetestans,exact_ode

0

(5)

A pair of infinitesimals for exact_ode are given by

sym:=symgenexact_ode

sym:=_ξ=0,_η=1yCx,y

(6)

Symmetries can be tested as well using symtest

symtestsym,exact_ode

0

(7)

See Also

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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