kill(all)$

appendix : a(x),b(x),simple result,version 1.0,part 3
peter.vlasschaert@gmail.com,15/03/2020

see : website 
4e) perturbation methods
-------------------------------
new: 05/03/2020:maxima:special:perturbation (=second order,nonlinear bvp),version 1.0,part1
download  (Maxima,code)       :maximaspecialperturbodesversion1finalpart1
download  (Maxima,png)         :maximaspecialperturbodesversion1finalpart1outp
new: 05/03/2020: example :variation parameter f(x) =perturb example,version 1.0,part2
download  (Maxima,code)       :maximavariationmethodextanxversion1testexamplepart2
download  (Maxima,png)         :maximavariationmethodextanxversion1testexamplepart2outp

1e) given system : 'a(x),b(x)'
----------------------

p1:sin(x)*'diff(b(x),x)-cos(x)*'diff(a(x),x) = 0;

p2:cos(x)*'diff(b(x),x)-sin(x)*'diff(a(x),x) = f(x);

p3:f(x) = cos(x)/(4*sin(2*x)+3*cos(2*x)+7);

p3a:subst([p3],p2);

2e) solve system for 'diff(a(x),x),'diff(b(x),x)
---------------------------------------------------- 

p3b:solve([p1,p3a],['diff(a(x),x),'diff(b(x),x)]);

p3c:flatten(p3b);

find :a(x)
-----------

p3c1a:p3c[1];

p3c1b:trigreduce(%);

p3c1c:integrate(%,x);

p1c1d:radcan(trigsimp(%));

find :b(x)
-----------

p3c2a:p3c[2];

p3c2b:trigreduce(%);

p3c2c:integrate(%,x);

p1c2d:radcan(trigsimp(%));