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

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

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. Use parentheses to clearly denote the argument of each function.$)$