Use the method for solving homogeneous equations $to$ solve the following differential equation.

$\frac{dx}{dt}=\frac{3x^2+7t\sqrt[\phantom{2}]{9t^2+x^2}}{3tx}$

Express the equation $in$ the form $\frac{dx}{dt}=F(\frac{x}{t}).$

$F(\frac{x}{t})=\frac{3(\frac{x}{t})+7\sqrt[\phantom{2}]{9+(\frac{x}{t}{)}^2}}{3(\frac{x}{t})}$