kill(all)$

appendix : maxima fvm : integration of differential , version 1.0
peter.vlasschaert@gmail.com,19/10/2022

How to use : antid,antidiff,integrate,to_poly_solve,at
---------------------------------------------------------------------

load(antid)$

→ diff(y(x),x,2)
---------------------

p1:diff(y(x),x,2);

p2:antidiff(p1,x,x);

p2:'integrate(p2,x,a,b) =integrate(p2,x,a,b);

p3:'integrate(antidiff(p1,x,x),x,a,b) =integrate(antidiff(p1,x,x),x,a,b);

→ d/dx(Γ*d(y(x))/dx)
-----------------------------

rem : Γ = Γ(x)

p1a:'diff(Γ(x)*diff(y(x),x),x) =diff(Γ(x)*diff(y(x),x),x) ;

p2a:integrate(lhs(p1a),x);

p2a1:at(p2a,x=a);

p2a2:'integrate(lhs(p1a),x,a,b) =at(p2a,x=b)-at(p2a,x=a);

p2b:antidiff(lhs(p1a),x,x);

p2b1:integrate(p2b,x,a,b);

p2b1a:args(p2b1);

you need use  "to_pöly_solve": complex equation = p2b2

solve : doesn't work.

p2b2:'diff(y(x)*Γ(x),x) =diff(y(x)*Γ(x),x) ;

p2b3:to_poly_solve(p2b2,p2b1a[1]);

rem : don't use "list" commands with %union

p2b4:part(p2b3,1);

use : p2b4 into p2b1

p3a:subst(p2b4,p2b1);

p3b:ev(p3a,integrate);

p3b1:ev(p3a,nouns);

p4a:rhs(p2b4[1]);

p4b:makelist(part(p4a,i),i,1,length(p4a));

p4c:sum(integrate(p4b[i],x,a,b),i,1,length(p4b));

rem : first part need  PI = partial integration method
----------------------------------------------------------------------

∈

→ integration

sa:'integrate(xˆ2*sin(x),x,0,1);

s1:factor(integrate(xˆ2*sin(x),x,0,1));

principal :
-------------

'diff(f*g) =ev('diff(f*g),nouns);

PI          : 
------------

source code: (p)artial (i)ntegration

idefparts(f,h,var,v1,v2):= block([g ],
g : integrate(h,var),
subst(v2,var, f*g) - subst(v1,var, f*g ) -
integrate(g*diff(f,var),var,v1,v2 ) )$

rem : g → local variable

s2:factor(idefparts(xˆ2,sin(x),x,0,1));

check : is
------------

s3:is(s1=s2);

info : antidiff & integrate

p4d:[part(p4c,1)];

remove : minus sign.

p4d1:args(part(p4d,1))[1];

→ integradum : p4d1

p4d2:args(p4d1)[1];

same result : integrate or antidiff

p4d3:integrate(p4d2,x);

p4d4:antidiff(p4d2,x,x);

------------------------------------------------------------------------------------