It is indicated the conditions on parameters $a_k^{(j)}$, under which a differential equation 

$z^3w''' + (a_1^{(2)}z^3 + a_2^{(2)}z^2)w'' + (a_1^{(1)}z^3 + a_2^{(1)}z^2 + a_3^{(1)}z)w' + (a_1^{(0)}z^3 + a_2^{(0)}z^2 + a_3^{(0)}z + a_4^{(0)})w = 0,$

has an entire solution close-to-convex in $\mathbb{D} = \{ z : |z| < 1\}$.

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