Use the substitution \(y=v x\) to find the solution of the differential equation
\(x \frac{\mathrm{~d} y}{\mathrm{~d} x}=y+\sqrt{9 x^{2}+y^{2}}\)
for which \(y=0\) when \(x=1\). Give your answer in the form \(y=\mathrm{f}(x)\), where \(\mathrm{f}(x)\) is a polynomial in \(x\).