Consider

\begin{align*}

dX_t=& Y_t dB_t + \frac12 X_t dt\\

dY_t=& X_t dB_t + \frac12 Y_t dt

\end{align*}

Show that \(X_t^2-Y_t^2\) is constant for all \(t\).

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\begin{align*}

dX_t=& Y_t dB_t + \frac12 X_t dt\\

dY_t=& X_t dB_t + \frac12 Y_t dt

\end{align*}

Show that \(X_t^2-Y_t^2\) is constant for all \(t\).