= Solution
For $0\le t\le T$, set $Z_t=\cosh x\,Y_t$. Part (b) gives $Z_0=1$, $\mathbb EZ_T=1$, and $Z_t>0$. Its stochastic differential is
$$
dZ_t=Z_t\eta_t\,dW_t,\qquad\eta_t=-\tanh X_t.
$$
Thus $Z$ is the <stochastic exponential> of $\int\eta\,dW$. The <Novikov condition> also holds, since $\exp(\frac12\int_0^T\eta_t^2dt)\le e^{T/2}$.
The <Girsanov theorem> says that under the measure with <Radon-Nikodym derivative> $Z_T$, the process $W_t-\int_0^t\eta_sds$ is a <Brownian motion> up to $T$. Substituting the sign of $\eta$ and the original <stochastic differential equation> gives
$$
\boxed{W_t^{\mathbb Q}=W_t+\int_0^t\tanh X_s\,ds=X_t-x.}
$$
The density is strictly positive, so $\mathbb Q$ and $\mathbb P$ are <equivalent probability measures>.
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