If `f(-x)=-f(x)` , then f(x) is

If a function satisfies f'(x)=f(x) ,then f(x)=

Solve (dy)/(dx) = yf^(')(x) = f(x) f^(')(x) , where f(x) is a given integrable function of x .

A function f satisfies the condition f(x)=f'(x)+f''(x)+f''(x)+…, where f(x) is a differentiable function indefinitely and dash denotes the order the derivative. If f(0) = 1, then f(x) is

Solve: (dy)/(dx)+y*f'(x)=f(x)*f'(x), where f(x) is a given function.

If f(x)=(x-1)/(x+1), then f(f(ax)) in terms of f(x) is equal to (a) (f(x)-1)/(a(f(x)-1)) (b) (f(x)+1)/(a(f(x)-1))(c)(f(x)-1)/(a(f(x)+1))(d)(f(x)+1)/(a(f(x)+1))

If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2)))^(2) and given that F(5) =5, then F(10) is

IF(f(x))^(4)=f((4x)), then (f'(4x))/(f'(x))= (i) (f(x))/(f(4x))(ii)(f(4x))/(f(x))(iii)f(x)f(4x)(iv)0