The variables \(x\) and \(y\) are related by the differential equation
\(4 \frac{\mathrm{~d}^{2} y}{\mathrm{~d} x^{2}}-y=3 .\)

It is given that, when \(x=0, y=-3\) and \(\frac{\mathrm{d} y}{\mathrm{~d} x}=2\).
(a) Find \(y\) in terms of \(x\).

(b) Deduce the exact value of \(x\) for which \(y=0\). Give your answer in logarithmic form.