A function `y=f(x)` satisfies `(x+1)f^(prime)(x)-2(x^2+x)f(x)=((e^x)^2)/((x+1)),AAx >-1.` If `f(0)=5,` then `f(x)` is

If f^(prime)(x)=x-1/(x^2) and f(1)=1/2 , find f(x) .

If f^(prime)(x)=x-1/(x^2) and f(1)=1/2 , find f(x) .

If the function f(x) satisfies (lim)_(x->1)(f(x)-2)/(x^2-1)=pi, evaluate (lim)_(x->1)f(x)

Let a function f(x) satisfies f(x)+f(2x)+f(2-x)+f(1+x)=x ,AAx in Rdot Then find the value of f(0)dot

A polynomial function f(x) satisfies the condition f(x)f(1/x)=f(x)+f(1/x) for all x inR , x!=0 . If f(3)=-26, then f(4)=

If f(x) is a function satisfying f(x)-f(y)=(y^y)/(x^x)f((x^x)/(y^y))AAx , y in R^*"and"f^(prime)(1)=1 , then find f(x)

If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f^(')(x)^(2)=0 AA x in R and f(0)=1=f^(')(0) . Then find f(x) .

If f^(prime)(x)=3x^2-2/(x^3) and f(1)=0 , find f(x) .

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then The value of lim_(x to -oo) f(x) is