You can 
put this solution on YOUR website! .
 = A*e^x - B*sin(x)
is the differential equation you are looking for.
 = A*e^x - B*sin(x)
is the differential equation you are looking for.
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Side note.    This fragment of the post   ". . . by eliminating the arbitrary constants"   MAKES  NO  SENSE.
The correct formulation is  THIS :
    For the given function  y =  Ae^x + Bcosx,  form a differential equation.
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You posted a series of posts with similar / (identical) passage.
I INSISTENTLY recommend you to RE-POST all these problems by EDITING them CORRESPONDINGLY.