"Nasser M. Abbasi" schrieb:   
   >   
   > [...]   
   >   
   > Thank you for your reply. Sorry, I had sign typo. It   
   > is "C-I" and not "C+I".   
   >   
   > I corrected it now and updated the link also. I also added   
   > screen shot from Kamke book showing the final solution it   
   > gives, which is the same.   
   >   
   > It is   
   >   
   > hand:=tan(x)+exp(-cos(x)^2)/( cos(x)^2*(_C1-int(exp(-cos(x)^2)/cos(x)^2,x)));   
   >   
   > Now Maple verifies my solution!   
   >   
   > odetest(y(x)=hand,eq);   
   >             0   
   >   
   > So now Maple says the "hand" solution satisfies the ODE.   
   >   
      
   For the record: Derive 6.10 cannot solve this differential equation.   
   Evaluating   
      
     DSOLVE1_GEN(-y^2 - y*SIN(2*x) - COS(2*x), 1, x, y, c)   
      
   immediately produces the string "inapplicable", and there seems to be   
   no specialized procedure that could succeed here.   
      
   Plugging your original   
      
     y := TAN(x)   
     + EXP(-COS(x)^2)/(COS(x)^2*(INT(EXP(-COS(x)^2)/COS(x)^2, x) + c))   
      
   into   
      
     DIF(y, x) - y^2 - y*SIN(2*x) - COS(2*x) = 0   
      
   shows that solution to be wrong, whereas the amended   
      
   y := TAN(x)   
     - EXP(-COS(x)^2)/(COS(x)^2*(INT(EXP(-COS(x)^2)/COS(x)^2, x) + c))   
      
   is found to satisfy the equation, reducing it to 0 = 0.   
      
   Martin.   
      
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