A functional equation

1. The problem statement, all variables and given/known data



Let [itex] a.b,c,d [/itex] be real numbers such that [itex] a ≠ b [/itex] and [itex] c ≠ 0 [/itex], find f:R->R for which this statement holds:



[tex] af(x+y) + bf(x-y) = cf(x) + dy [/tex] , for all x,y real numbers.







2. Relevant equations



Well this is a functional equation, that I know. I have less experience with those type of euqations.





3. The attempt at a solution



I tried to plug in some values:



for x = y: [tex] af(2x)=cf(x)+dx-bf(0) [/tex]



for x = y = 0 :[tex] af(0) + bf(0) = cf(0) [/tex]



I don't know what to do next, and how could these facts can help me. Can anyone help me solve this problem, please :D ?