  The short article [V.M. Buchstaber, E.Yu. Netay,
$\mathbb{C}P(2)$-multiplicative Hirzebruch genera and elliptic cohomology,
Russian Math. Surveys, 69:4 (2014), 757-759] states results on
$\mathbb{C}P(2)$-multiplicative Hirzebruch genera. The aim of the following
text is to give a proof of Theorem 3. This proof uses only the technique of
functional differential equations.
