= Solution
{c}
The bounded integrand makes $X_s=\int_0^sY_u\,dW_u$ a square-integrable martingale, with <quadratic variation>
$$
\langle X\rangle_s=\int_0^sY_u^2du\leq C^2t\qquad(s\leq t).
$$
Thus
$$
\mathbb E\exp\bigl(\tfrac12\langle X\rangle_t\bigr)\leq e^{C^2t/2}<\infty.
$$
<Novikov's condition> applies to the <stochastic exponential> $Z_s=\exp(X_s-\langle X\rangle_s/2)$. Hence \b[$Z$ is a true martingale with $\mathbb E Z_s=Z_0=1$]. It is strictly positive because its exponent is finite almost surely.
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