= Solution
<Moser theorem> says that if $M$ is a <compact> <smooth manifold> without boundary and $\omega_t$, $0\leq t\leq1$, is a smooth family of <symplectic forms> with constant <de Rham cohomology> class, then there is a <smooth isotopy> $\psi_t$, with $\psi_0=\mathrm{id}$, such that
$$
\boxed{\psi_t^*\omega_t=\omega_0.}
$$
Thus the endpoints are <symplectomorphic>. The hypothesis is a whole path of <symplectic forms>, not merely equality of the endpoint <de Rham cohomology> classes.
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