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 function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,

An even polynomial function f(x) satisfies a relation f(2x)(1-f(1/(2x)))+f(16x^2y)=f(-2)-f(4x y)AAx ,y in R-{0}a n df(4)=-255 ,f(0)=1. Then the value of |(f(2)+1)//2| is_________

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)=2 , then

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 the function f(x) satisfies lim_(xrarr1)(f(x)-2)/(x^(2)-1)=pi , evaluate lim_(xrarr1)f(x) .

A function f satisfies the condition f(x)=f^(prime)(x)+f^(primeprime)(x)+f^(primeprimeprime)(x) ...... ,where f(x) is a differentiable function indefinitely and dash denotes the order of derivative. If f(0)=1,t h e nf(x) is (A) e^(x/2) (B) e^x (C) e^(2x) (D) e^(4x)

A Function f(x) satisfies the relation f(x)=e^x+int_0^1e^xf(t)dtdot Then (a) f(0) 0

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a) f''(x)=f(x)=0 (b) 4f''(x)+f(x)=0 (c) f''(x)+f(x)=0 (d) 4f''(x)-f(x)=0

A continuous function f(x)onRvec satisfies the relation f(x)+f(2x+y)+5x y=f(3x-y)+2x^2+1forAA x ,y in RdotT h e n findf(x)dot

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=