If f(x+y) = f(x).f(y) then f(x)=ax

If f(x+y) = f(x)+f(y) then f(x)=kx

If f(xy) = f(x)+f(y) then f(x)=log x

If f(xy) = f(x).f(y) then f(x)=xn

If f(x+y) = f(x)=f(y), then f(x)=k

If f(x).f(1/x)=f(x)+f(1/x), then f(x)=xn+1

If f(x+y) + f(x-y) = 2f(x)f(y) then f(x)=(ax + a-x)/2

If f(x) is a function such that f(x)f(y)-(f(xy)+f(1/y))/2 = 0 then f(x) = cos(log x)

If f(x+y) =  f(x)+f(y) then  f(n)=n.f(1) ]

Eq.Of The Curve                                                           Diff.Eq
 
1.y=c1eAx+c2eBx                                                                d2y/dx2-(A+B)dy/dx+
(where c1,c2 are arbitary                                       (AB)y=0
Const?s)
 
2. y=eAx(c1x+c2)                                               d2y/dx2-2Ady/dx+A2y=0
 
3.y=eAx(c1cosBx+c2sinBx)                                d2y/dx2- 2Ady/dx+
                                                                         (A2+B2)y=0
 
4.y=c1xm+c2xn                                                  x2d2y/dx2-(m+n-1)
                                                                          Xdy/dx+mny=0
 
5.y=c1eAx+c2eBx+c3eCx                                    d3y/dx3-(A+B+C)d2y/dx2

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