Find the function y=y(x)\displaystyle {y}={y}{\left({x}\right)} (for x>0\displaystyle {x}\gt{0}) which satisfies the separable differential equation

dydx=7+12xxy2   x>0\displaystyle \frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}=\frac{{{7}+{12}{x}}}{{{x}{y}^{{2}}}}\ \ \ {x}\gt{0}

with the initial condition y(1)=6\displaystyle {y}{\left({1}\right)}={6}.

y=\displaystyle {y}=