(Solved): Use the method for solving homogeneous equations to solve the following differential equation. \[ \ ...

Use the method for solving homogeneous equations to solve the following differential equation. \[ \frac{d x}{d t}=\frac{4 x^{2}+9 t \sqrt{6 t^{2}+x^{2}}}{4 t x} \] Ignoring lost solutions, if any, an implicit solution in the form \( \mathrm{F}(\mathrm{t}, \mathrm{x})=\mathrm{C} \) is \( \quad=\mathrm{C} \), where \( \mathrm{C} \) is an arbitrary constant. (Type an expression using \( x \) and \( t \) as the variables.)