Let `y=f(x)` satisfies `(dy)/(dx)=(x+y)/(x)` and `f(e)=e ` then the value of `f(1)` is

If y satisfies (dy)/(dx)=(e^(y))/(x^(2))-(1)/(x) and y(1)=0 then the value of e^(y(2)) is

Let y=f (x) and x/y (dy)/(dx) =(3x ^(2)-y)/(2y-x^(2)),f(1)=1 then the possible value of 1/3 f(3) equals :

If y=f(x) satisfy differential equation ( dy )/(dx)-y=e^(x) with f(0)=1 then value of f'(0) is

Let f(x) be defined for all x>0 and be continuous.Let f(x) satisfies f((x)/(y))=f(x)-f(y) for all x,y and f(e)=1. Then (a) f(x) is bounded (d) (b) f((1)/(x))vec 0 as xvec 0 (c) f(x) is bounded (d) f(x)=(log)_(e)x

Let f(x) be continuous and differentiable function everywhere satisfying f(x+y)=f(x)+2y^(2)+kxy and f(1)=2, f(2)=8 then the value of f(3) equals

A function y=f(x) satisfies the differential equation (dy)/(dx)+x^(2)y+2x=0,f(1)=1 then the value of f(1) is-

Let f be a continuous function satisfying f(x + y) = f (x) f( y) (x, y in R) with f(1) = e then the value of int(xf(x))/(sqrt(1+f(x)))dx is

Let y=f(x) satisfy the differential equation (dy)/(dx)=(x+y)/(x),y(1)=1, then y((1)/(e)) is equal

If y=f (x) satisfy the differential equation (dy)/(dx) + y/x =x ^(2),f (1)=1, then value of f (3) equals: