= Solution
{c}
Vary the <action>, taking the field variation to vanish at the boundary. <Integration by parts> gives
$$
\delta S_0=\int d^4x\left[\partial^\mu\phi\,\partial_\mu\delta\phi-m^2\phi\delta\phi-\frac\lambda6\phi^3\delta\phi\right]
=-\int d^4x\left(\Box\phi+m^2\phi+\frac\lambda6\phi^3\right)\delta\phi.
$$
Thus the <Euler-Lagrange field equation> is
$$
\boxed{\Box\phi+m^2\phi+\frac\lambda6\phi^3=0.}
$$
For the <field redefinition> in part <1/f>, define the <functional derivative> $E(\phi)=\delta S_0/\delta\phi=-(\Box\phi+m^2\phi+\lambda\phi^3/6)$. The sign does not affect the <equation of motion>, but it fixes the sign of an added <redundant operator>.
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