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Consider the following system of coupled differential equations:$$\begin{cases}\dfrac{dx}{dt} = y^2 \\ \dfrac{dy}{dt} = x\end{cases}$$Show that the functions defined by \(x(t) = -\dfrac{12}{t^3}\) and \(y(t) = \dfrac{6}{t^2}\) form a valid solution to this system for \(t \neq 0\).
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