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

$\frac{dx}{dt}=\frac{9x^2+8t\sqrt[\phantom{2}]{4t^2+x^2}}{9tx}$

Ignoring lost solutions, if any, an implicit solution in the form $F(t,x)=C$ is $,C,$ where $C$ is an arbitrary constant. $($Type an expression using $x$ and $t$ as the variables.$)$