dintegrate2

#:mode=maple:

getdepvar := proc ( fn ) op ( 0, fn ) end;
getindepvar := proc ( fn ) op ( fn ) end;


dintegrate_2_g3_13 := proc ( deq, fn, jb, fs, ccoordl )

local	sl,
		inv2,
		lt,
		phii,
		degr,
		anscfs,
		deq0, deq01,
		ansz,
		dits,
		cmp,
		cfs,
		res,
		loes,
		i,
		x, y;
		
global XX, YY;

x := getindepvar ( fn );
y := getdepvar ( fn );

sl := ccoordl;

inv2 := fn^3 * diff ( fn, x, x );

lt := diff ( fn, x, x );
degr := degree ( deq, lt );

anscfs := [seq ( _CC||i, i = 0..degr )];


deq0 := [seq ( anscfs[i+1] * phii^i , i = 0..degr )];
deq0 := convert ( deq0, `+` );
deq01 := deq0;

deq0 := subs ( phii=inv2, deq0 );
ansz := dtrans ( sl, deq0 );

cmp := dnormal ( ansz - deq );

dits := dindets ( cmp, [fn] );
dits := rawsort ( dits );

cmp := collect ( cmp, dits, distributed );
cfs := coeffs ( cmp, dits );

res := map ( (xx,cc) -> [op(solve ( identity(xx = 0,x ), cc ))], [cfs], {op(anscfs)} );
res := flatten2 ( res );
res := select ( type, res, name = constant );
res := [op({op(res)})];

deq01 := subs ( res, deq01 );
deq01 := map ( (z,w)-> w = z, [solve ( deq01, phii )], phii );
deq01 := subs ( phii=inv2, deq01 );

loes := map( (z,ff) -> dsolve ( z, ff ), deq01, fn );

loes := map ( x-> lhs(x)-rhs(x), loes );

loes := map ( (x,s)->dtrans ( s, x, full ), loes, sl );

loes := dnormal ( loes );

loes;

end;

#
#

dintGetOmega := proc ( deq, fn, invarlis, ccoordl )

local ivl1, ivl,
		e,
		dits, dxlt,
		i,
		ee;

ivl1 := map ( (X,Y)->lhs(X)-dtrans ( Y, rhs(X), full ), invarlis, ccoordl );

ivl := [];

for e in ivl1 do

	e := normal ( e );

	dits := dindets ( e, [fn] );
	dits := rawsort ( dits );
	dxlt := dits[1];
	
	ivl := [op(ivl), dxlt = solve ( e, dxlt )];

od;

ee := deq;

for i from nops ( ivl ) to 1 by -1 do

	ee := subs ( ivl[i], ee );
	
	ee := dsimplify ( ee, symbolic );
	
od;

RETURN ( ee );

end;