If $2xf ' (x) - f(x) = 0$ find $f$ So $2xf '(x) - f(x) = 0$ and we know that $f(1) =1$. So I actually need to find the integral of $2xf'(x) - f(x)$.
Thanks.

$$\frac{f'(x)}{f(x)}=\frac{1}{2x} \Rightarrow \ln|f(x)|=\frac{1}{2} \ln{x} +c \Rightarrow \ln|f(x)|= \ln{{x}^{\frac{1}{2}}} +c \Rightarrow f(x)= \pm c_1 \sqrt{x} \Rightarrow f(x)=C \sqrt{x}$$ 
$$f(1)=1 \Rightarrow 1= C $$
So $$f(x)=\sqrt{x}$$
