= Solution
The classical equations are
$$
(\Box+M^2)\phi+\lambda\bar\psi\psi=0,
\qquad
(i\not\partial-m-\lambda\phi)\psi=0,
\qquad
i(\partial_\mu\bar\psi)\gamma^\mu+m\bar\psi+\lambda\phi\bar\psi=0.
$$
For any time-ordered functional $\mathcal O$, the three <Schwinger-Dyson equations> state that insertion of each left-hand side equals the corresponding contact terms obtained by $-i$ times the functional derivative of $\mathcal O$ with respect to $phi$, $\bar\psi$, or $\psi$, with the usual reversed order and Grassmann signs for fermionic derivatives.
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