A differential equation is given by ${\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x} = e^{ 4y }.}$

(a) Find the general solution of the differential equation, leaving your answer in the form ${y=f(x).}$

(b) Find the particular solution given that ${y=0}$ when ${x=\frac{1}{2}.}$

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