kill(all)$

maxima : simple linear integral equation ( = exact solution),part 1,version 1.0
peter.vlasschaert@gmail.com, 10/03/2022

load packages ,option
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load(lrats)$ratprint:false$

given : simple integral equation
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p1a:y(x) =1+'integrate('x*t*y(t),t,0,1);

rem: simple integral equation,second order fredholm integral equations.

→ first step : find integral "p1a",here coef from x in rhs (see:given)

p1b:C=ratcoeff(rhs(p1a),x);

rem : integral between fixed boundary value integral constant = C
C =unknown

→second step: back subst "p1a"

p1c:subst([reverse(p1b)],p1a);

→thrid step : find  y(t) "p1c", x=t

p1d:subst([x=t],p1c);

→fourth step :subst "p1d" into "p1b"

p1e:subst([p1d],p1b);

→fifth step : ev "p1e",nouns

p1f:ev(p1e,nouns);

→sixth step : solve "p1f",C

p1g:solve(p1f,lhs(p1b));

final result :

→ seventh step:subst,"p1c",C

p1h:subst(p1g,p1c);

check result : "p1h"

a)  subst : "p1h", x=t

q1a:subst([x=t],p1h);

b) subst,"p1h" and "q1a" into "p1a"

q1b:subst([p1h,q1a],p1a);

c) ev, "q1b",nouns

q1c:ev(q1b,nouns);

q1c2:is(q1c);