Solve: `dy/dx=(y f\'(x)-y^2)/f(x)`, where `f(x)` is a given function of `x`

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

Solve (dy)/(dx)=(yphi'(x)-y^(2))/(phi(x)),"where" " "phi(x) is a given function.

Solve: (dy)/(dx) = (yf^(')(x)-y^(2))/(f(x))

dy/dx+y f\'(x)-f(x)f\'(x)=0

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

Solve (dy)/(dx)+y phi'(x)=phi(x).phi'(x), "where" " "phi(x) is a given function.

Let f (x) = a ^ x ( a gt 0 ) be written as f ( x ) = f _ 1 (x ) + f _ 2 (x) , where f _ 1 ( x ) is an even function and f _ 2 (x) is an odd function. Then f _ 1 ( x + y ) + f _ 1 ( x - y ) equals :

Let f(x)=a^(x)(a gt 0) be written as f(x)=f_(1)(x)+f_(2)(x), " where " f_(1)(x) is an function and f_(2)(x) is an odd function. Then f_(1)(x+y)+f_(1)(x-y) equals

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b

A real valued function f(x) satisfies the functional equation f(x-y)=f(x)f(y)-f(a-x)f(a+y) where a is a given constant and f(0), f (2a-x)=