Resol ax/at+tx=(t*x)^s

$$\frac { a x } { a t } + t x = ( t \cdot x ) ^ { s }$$

Resoleu s (complex solution)

$$\left\{\begin{matrix}s=\log_{tx}\left(tx+\frac{x}{t}\right)+\frac{2\pi n_{1}i}{\ln(tx)}\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 0\text{ and }t\neq 0\text{ and }t\neq -i\text{ and }t\neq i\text{ and }x\neq \frac{1}{t}\text{ and }a\neq 0\\s\in \mathrm{C}\text{, }&x=0\text{ and }t\neq 0\text{ and }a\neq 0\end{matrix}\right,$$

Resoleu s

$$\left\{\begin{matrix}s=\log_{tx}\left(tx+\frac{x}{t}\right)\text{, }&x\neq \frac{1}{t}\text{ and }x\neq 0\text{ and }\left(x<0\text{ or }t>0\right)\text{ and }\left(t<0\text{ or }x>0\right)\text{ and }t\neq 0\text{ and }a\neq 0\\s>0\text{, }&a\neq 0\text{ and }t\neq 0\text{ and }x=0\end{matrix}\right,$$