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It is proved in this paper that the maximum number of limit cycles of system
⎧ dx/dt = y
⎨
⎩ dy/dt = kx - (k + 1)x2 + x3 + ε(α + βx + γx2)y
is equal to two in the finite plane, where k > (11 + √33) / 4 , 0 < |ε| << 1, |α| + |β| + |γ| ≠ 0. This is partial answer to the seventh question in [2], posed by Arnold.
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