O17-C029
> restart:
> ed1:=diff(y(x),x$2)+exp(I*x)*diff(y(x),x)+y(x)=0;

                 / 2      \
                 |d       |            /d      \
          ed1 := |--- y(x)| + exp(x I) |-- y(x)| + y(x) = 0
                 |  2     |            \dx     /
                 \dx      /

> ed2:=diff(y(x),x$2)+exp(I*x)*diff(y(x),x)+y(x)=exp(-I*x);

             / 2      \
             |d       |            /d      \
      ed2 := |--- y(x)| + exp(x I) |-- y(x)| + y(x) = exp(-I x)
             |  2     |            \dx     /
             \dx      /

> s1:=dsolve(ed1,y(x));

   s1 := y(x) = _C1 (1 - exp(-I x) I) + _C2 exp((-x + exp(x I)) I)

> dsolve(ed2,y(x));

  y(x) = (1 - exp(-I x) I) _C2 + exp((-x + exp(x I)) I) _C1

         - 1/2 Ei(1, exp(x I) I) exp((-x + exp(x I)) I)

> varcons:=subs(s1,_C1=a,_C2=b,y(x));

      varcons := a (1 - exp(-I x) I) + b exp((-x + exp(x I)) I)

> varcons2:=diff(varcons,x)=exp(-I*x);

  varcons2 :=

        -a exp(-I x) + b (-1 + exp(x I) I) exp((-x + exp(x I)) I) I

         = exp(-I x)

> resol:=solve({varcons,varcons2},{a,b});

                               exp(-I x)
  resol := {a = - ------------------------------------, b = -
                  -I - exp(x I) + exp(x I) exp(-I x) I

        (-1 + exp(-I x) I) exp(-I x)/(exp((-x + exp(x I)) I)

        (-I - exp(x I) + exp(x I) exp(-I x) I))}

> cprim1:=unapply(subs(resol,a),x);cprim2:=unapply(subs(resol,b),x);

                                      exp(-I x)
        cprim1 := x -> - ------------------------------------
                         -I - exp(x I) + exp(x I) exp(-I x) I


  cprim2 := x -> - (-1 + exp(-I x) I) exp(-I x)/(

        exp((-x + exp(x I)) I) (-I - exp(x I) + exp(x I) exp(-I x) I)

        )

> c1:=int(cprim1,0..x);

              c1 := -1/2 I (exp(2 I x) - 1) exp(-2 I x)

> c2:=int(cprim2,0..x);
Warning, unable to determine if 1/2*Pi+Pi*_Z1 is between 0 and x; try to use assumptions or set _EnvAllSolutions to true


           x
          /
         |
  c2 :=  |   - (-1 + exp(-I _X) I) exp(-I _X)/(
         |
        /
          0

        exp((-_X + exp(_X I)) I)

        (-I - exp(_X I) + exp(_X I) exp(-I _X) I)) d_X

>