1.14: Implicit differentiation and a normal

Given that

(a) show that

(b) Find the value of $\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x}$ when $\displaystyle x=0$.

(c) Find an equation of the normal to the curve with equation $\displaystyle 2xy+5y=\mathrm{e}^x$ at the point where $\displaystyle x=0$. Give your answer in the form

where $\displaystyle p$, $\displaystyle q$ and $\displaystyle r$ are integers.