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The general solution of the differential equation $\frac{d x}{d t}=\frac{x \log x}{t}$ is
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$\mathrm{e}^{\mathrm{ct}}=\mathrm{x}$
$\begin{aligned} & \frac{d x}{d t}=\frac{x \log x}{t} \\ & \therefore \int \frac{d x}{x \log x}=\int \frac{d t}{t} \\ & \therefore \log |\log x|=\log |t|+\log c \\ & \therefore \log x=t c \Rightarrow x=e^{t c}\end{aligned}$
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