(a) Show that \((\cosh x+\sinh x)^{\frac{1}{2}}=\mathrm{e}^{\frac{1}{2} x}\).
(b) Find the particular solution of the differential equation
\(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}+\frac{\mathrm{d} y}{\mathrm{~d} x}+3 y=5(\cosh x+\sinh x)^{\frac{1}{2}}\)
given that, when \(x=0, y=1\) and \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{4}{3}\).