formula

$X_t&=&u(W_t,Y_t)\\ &=&\frac{1}{2}\bigg\{(\sqrt{1+Y_t^2}+Y_t)e^{W_t}-(\sqrt{1+Y_t^2}-Y_t)e^{-W_t} \bigg\}\\ &=&\frac{1}{2}\bigg\{(\sqrt{1+\xi^2}+\xi)e^{t+W_t} -(\sqrt{1+\xi^2}-\xi)e^{-t-W_t}\bigg\}$